WEBVTT
Kind: captions
Language: en
00:00:01.760 --> 00:00:04.960
okay so webassign problem we had the other day is
00:00:05.380 --> 00:00:06.340
on january 1st
00:00:10.100 --> 00:00:11.060
deposit 1 cent
00:00:14.960 --> 00:00:16.200
on january 2nd, deposit 3 cents
00:00:16.880 --> 00:00:17.680
january 3rd
00:00:19.520 --> 00:00:20.560
deposit 9 cents
00:00:20.900 --> 00:00:22.820
which you could also think of
00:00:24.200 --> 00:00:24.840
as 3 cents
00:00:26.760 --> 00:00:28.120
squared. january 4th
00:00:29.900 --> 00:00:31.180
youre gonna put .09
00:00:31.780 --> 00:00:32.820
tripled right?
00:00:34.120 --> 00:00:36.360
dont think of that formula squared, excuse me
00:00:39.140 --> 00:00:42.180
thats... put in one cent
00:00:42.400 --> 00:00:44.080
the next thing you put in you triple it
00:00:45.420 --> 00:00:47.900
so you can think of that as .01, times 3
00:00:48.860 --> 00:00:50.300
then you put in 9 cents
00:00:51.020 --> 00:00:52.620
you can think of it as .01
00:00:54.040 --> 00:00:55.480
times 3, times 3 again
00:00:57.200 --> 00:00:59.040
or .01
00:01:00.680 --> 00:01:01.720
times 3 squared
00:01:02.180 --> 00:01:03.820
this is what makes it exponential
00:01:05.040 --> 00:01:05.600
next day
00:01:08.120 --> 00:01:10.760
.27 seconds instead we can say .01cents
00:01:11.880 --> 00:01:12.760
times 3 cubed
00:01:14.860 --> 00:01:21.340
each day were multiplying by 3, the number you put in the previous day. the states are exponential
00:01:23.760 --> 00:01:26.240
so 1 cent times 3, 1 cent times 3 times 3
00:01:26.240 --> 00:01:27.980
1 cent times 3 times 3 times 3
00:01:28.720 --> 00:01:29.840
so on the 10th day
00:01:32.160 --> 00:01:33.680
your gonna put in 1 cent
00:01:35.000 --> 00:01:36.600
3 times 3 times 3, 9 times
00:01:38.760 --> 00:01:40.520
now you just have to know what 3 to the 9 is
00:01:41.340 --> 00:01:43.740
which you can find with a calculator
00:01:43.740 --> 00:01:45.560
if this were a test question
00:01:45.560 --> 00:01:46.600
this would be the answer
00:01:50.480 --> 00:01:52.880
from the 30th day thats a lot of money
00:01:54.160 --> 00:01:56.080
3 to the 30 is a very big number
00:01:58.220 --> 00:02:00.560
okay, everyone understand how to do that on webassign?
00:02:02.260 --> 00:02:03.460
okay with that one
00:02:09.560 --> 00:02:11.640
another type of thing we had was
00:02:11.640 --> 00:02:14.220
was i doing half life problems last time?
00:02:15.380 --> 00:02:18.340
you were doing half life in chemistry right?
00:02:19.640 --> 00:02:20.280
half life
00:02:20.280 --> 00:02:23.740
no you didnt do that in high school chemistry? maybe do that in physics
00:02:24.420 --> 00:02:26.660
so you have radioactive elements
00:02:29.420 --> 00:02:31.020
they change, they decay
00:02:31.360 --> 00:02:32.880
so you have the nucleus
00:02:33.160 --> 00:02:35.000
and the nucleus is unstable
00:02:35.080 --> 00:02:36.360
and what happens is
00:02:37.280 --> 00:02:39.520
some of the elements in the nuclei
00:02:40.620 --> 00:02:42.860
break down into different nuclei
00:02:42.860 --> 00:02:45.280
and this is called radioactive decay
00:02:46.600 --> 00:02:49.400
you can omit alpha, bata, or gama partical
00:02:49.400 --> 00:02:50.660
it doesnt really matter
00:02:50.660 --> 00:02:51.860
you get through this lecture
00:02:52.040 --> 00:02:53.080
what happens is
00:02:53.080 --> 00:02:55.980
you can look at the portions you had at the beginning
00:02:55.980 --> 00:02:57.720
and what you had at a later amount of time
00:02:57.720 --> 00:02:59.920
you need to figure out how much time has pasted
00:02:59.920 --> 00:03:01.680
so thats called the half life
00:03:02.020 --> 00:03:04.660
half life is how long it takes to get half
00:03:04.660 --> 00:03:06.100
of what you had before
00:03:07.360 --> 00:03:08.320
so carbon date
00:03:09.020 --> 00:03:10.700
carbon 14 is radioactive
00:03:11.320 --> 00:03:13.000
and turns to the carbon 12
00:03:13.000 --> 00:03:15.540
you know what the 14 and 12 stand for right?
00:03:17.400 --> 00:03:19.560
so what happens is it changes and
00:03:19.560 --> 00:03:22.520
and it has a certain amount of time so the half life
00:03:23.000 --> 00:03:24.360
make up some element
00:03:24.980 --> 00:03:26.660
and lets say the half life
00:03:34.980 --> 00:03:35.540
is 5 days
00:03:59.860 --> 00:04:03.340
so what fraction or what percentage will be remaining after 20 days
00:04:03.900 --> 00:04:08.060
when i ask for percentage, what you should do is start with a 100
00:04:13.100 --> 00:04:13.600
day 0
00:04:14.300 --> 00:04:15.580
i have 100 whatever
00:04:16.220 --> 00:04:16.720
grams
00:04:17.600 --> 00:04:19.860
doesnt matter cause ill be at percent, 100 percent
00:04:21.260 --> 00:04:24.140
so after 5 days i have half as much so i have 50
00:04:25.520 --> 00:04:26.720
or as i said before
00:04:28.520 --> 00:04:29.160
50 right?
00:04:29.160 --> 00:04:30.720
so you got to figure it out
00:04:31.400 --> 00:04:32.440
so after 10 days
00:04:33.740 --> 00:04:36.240
i have 25 lefte
00:04:41.560 --> 00:04:44.520
thats what the half life means, after 15 days
00:04:45.800 --> 00:04:46.300
i have
00:04:48.060 --> 00:04:48.560
12.5
00:04:49.300 --> 00:04:49.860
per cent
00:04:49.860 --> 00:04:55.300
so what we can do is measure percisly how much carbon you had before and how much you had after
00:04:56.700 --> 00:04:59.100
the carbon by the way is only good for
00:05:00.040 --> 00:05:02.120
50 thousand years or something
00:05:02.120 --> 00:05:05.480
100 thousand years, its not really good till a million
00:05:05.600 --> 00:05:09.760
very multi million years old, then you use different elements
00:05:09.760 --> 00:05:11.320
always take a break down
00:05:12.340 --> 00:05:15.140
so half a uranium is half of the earth so you
00:05:15.140 --> 00:05:16.980
can use uranium more easily
00:05:19.000 --> 00:05:19.500
20 days
00:05:20.600 --> 00:05:21.800
youre down to 6.25
00:05:22.960 --> 00:05:25.440
so what percent remains at the 20 days
00:05:26.840 --> 00:05:27.340
6.25
00:05:28.320 --> 00:05:28.880
percent
00:05:31.720 --> 00:05:33.720
so another way to think of this
00:05:33.860 --> 00:05:36.020
is you can say the amount you have
00:05:37.480 --> 00:05:38.920
is 100, percent is 100
00:05:40.320 --> 00:05:41.040
times 1/2
00:05:44.760 --> 00:05:46.120
t/5, so why is it t/5?
00:05:48.080 --> 00:05:49.840
when t is 5, you get a 1/2 of 1
00:05:52.380 --> 00:05:53.100
when t is 10
00:05:54.300 --> 00:05:55.100
you get a 1/2
00:05:56.140 --> 00:05:57.660
would be 10/5, 10/5 is 2
00:05:57.660 --> 00:05:59.260
so you get a half of a half
00:06:00.300 --> 00:06:01.420
that make sense?
00:06:02.700 --> 00:06:03.420
when t is 15
00:06:05.080 --> 00:06:05.640
15/5 is 3
00:06:06.180 --> 00:06:08.900
so you get a 1/2 of a 1/2 of a 1/2, a 1/2 cubed
00:06:10.360 --> 00:06:12.680
it makes it an exponential formula
00:06:14.640 --> 00:06:16.020
just like one of those exponential formulas
00:06:21.180 --> 00:06:23.900
well if you were given a half life in years
00:06:23.900 --> 00:06:25.660
then t would be measured in years
00:06:26.220 --> 00:06:29.900
so you want to make sure you match whatever the units are
00:06:31.860 --> 00:06:33.380
want to match the units
00:06:35.120 --> 00:06:37.600
what ever the half life is measured in
00:06:37.740 --> 00:06:43.500
if its measured in nano seconds, or measured in years the t should be a multiple of a half
00:06:45.160 --> 00:06:47.080
so when t equals the half life
00:06:47.080 --> 00:06:49.980
you cut it in half once, since you double a half life
00:06:50.980 --> 00:06:53.220
you now have 1/2, 1/2 which is a 4th
00:06:55.740 --> 00:06:57.660
so general way to do half life
00:07:04.000 --> 00:07:04.500
i assume you did this in chemistry
00:07:07.480 --> 00:07:09.720
the amount that you have times the
00:07:09.860 --> 00:07:11.700
is the amount you start with
00:07:12.820 --> 00:07:13.460
times 1/2
00:07:15.840 --> 00:07:16.340
t/k
00:07:17.460 --> 00:07:18.580
k is the half life
00:07:55.860 --> 00:07:56.980
we love pre calc?
00:07:58.040 --> 00:07:58.540
no love
00:07:59.020 --> 00:08:00.780
no love for pre calc either
00:08:15.200 --> 00:08:19.320
so you can do a half life question, something like this can easily show up on the exam
00:08:21.040 --> 00:08:21.760
i could say
00:08:23.640 --> 00:08:25.080
im gonna cover this up
00:08:30.000 --> 00:08:30.500
les see
00:09:25.480 --> 00:09:28.560
the half life of an element is 6 hours, so theres 400 grams originally
00:09:28.760 --> 00:09:31.320
the amount you would have woulld be 400
00:09:32.180 --> 00:09:32.820
times 1/2
00:09:34.160 --> 00:09:34.720
to the 10
00:09:35.640 --> 00:09:36.140
over 6
00:09:36.980 --> 00:09:39.220
do you know what 1/2 to the 10/6 is?
00:09:40.760 --> 00:09:41.480
no you dont
00:09:44.240 --> 00:09:45.660
i mean how are you suppose to figure that out?
00:09:49.040 --> 00:09:50.240
i dont know how youre suppose to figure that out
00:09:51.980 --> 00:09:52.860
i mean its 1/2
00:09:53.640 --> 00:09:54.760
raised to the 5/3
00:09:54.760 --> 00:09:56.400
so you take the cubed root of 1/3
00:09:56.940 --> 00:09:58.780
and then you raise it to the 5
00:09:59.160 --> 00:10:02.280
this is not fu, this is what calculators are for
00:10:02.280 --> 00:10:05.500
so if we gave a question that looked like that, thats all we expected
00:10:05.500 --> 00:10:07.640
just show you know how to find the half life
00:10:07.640 --> 00:10:10.680
of course you can take this and make it a slighly harder problem
00:10:11.540 --> 00:10:12.420
we all go that
00:10:19.820 --> 00:10:21.740
um you just have to write that
00:10:24.080 --> 00:10:24.580
so
00:10:37.920 --> 00:10:39.440
a new variation of this
00:11:38.620 --> 00:11:41.500
originally you have 180 grams of an element
00:11:43.100 --> 00:11:45.420
and after 6 hours, you have 40 grams
00:11:45.960 --> 00:11:49.560
of the element, how many would you have after 20 hours?
00:11:49.940 --> 00:11:53.620
so this is not quite a half life, but you can do a half life
00:11:53.780 --> 00:11:56.980
but its easier to do it as an exponential problem
00:11:58.180 --> 00:11:59.860
so lets say how we can do it
00:12:03.580 --> 00:12:06.860
you dont have to do it for the 1/2 if you dont want to
00:12:08.120 --> 00:12:09.800
you can do it instead with
00:12:11.380 --> 00:12:11.880
a and b
00:12:12.680 --> 00:12:16.920
so a nice way to do exponentials, all exponentials are the form y
00:12:18.020 --> 00:12:18.900
equals some a
00:12:18.900 --> 00:12:19.880
00:12:19.880 --> 00:12:23.240
times some b to the x, or t, whatever number you love
00:12:23.240 --> 00:12:26.600
a and b are constant, so we can use this information
00:12:26.800 --> 00:12:28.080
to figure out a and b
00:12:30.420 --> 00:12:35.780
so originally you have 180 grams of an element, and after 6 hours you have 40 grams
00:12:35.780 --> 00:12:39.500
how many do you have after 20 hours, well that tells you that
00:12:40.180 --> 00:12:40.680
after
00:12:42.720 --> 00:12:44.080
you originally have
00:12:46.500 --> 00:12:47.380
times 0 is 180
00:12:49.700 --> 00:12:51.540
and then times 6, you have 40
00:12:51.900 --> 00:12:56.380
so thats a pair of coordinates, so this is like the homework problem
00:12:56.380 --> 00:13:00.040
so now we can figure out what a and b are from the coordinates
00:13:02.560 --> 00:13:04.320
so when x is 0 y is 180, so 180
00:13:06.220 --> 00:13:07.420
is a times b to the 0
00:13:09.020 --> 00:13:10.620
but anything to the 0 is 1
00:13:13.020 --> 00:13:13.660
so 180 is a
00:13:14.300 --> 00:13:16.940
so now you can rewrite the equation, so y
00:13:18.760 --> 00:13:20.200
is 1180 times b to the x
00:13:21.180 --> 00:13:22.940
okay does that make senes?
00:13:23.880 --> 00:13:25.160
so agin, when be is 0
00:13:25.920 --> 00:13:26.720
you have 180
00:13:27.780 --> 00:13:30.020
plug in 0 and 180, anything to 0 is 1
00:13:30.960 --> 00:13:34.000
so now you now know a so go back to your equation
00:13:34.100 --> 00:13:35.540
and replace a with 180
00:13:37.120 --> 00:13:39.200
we got half of the equation done
00:13:40.800 --> 00:13:41.520
now you say
00:13:42.220 --> 00:13:43.820
when x is 6 i have to get 40
00:13:44.920 --> 00:13:45.420
so 40
00:13:46.520 --> 00:13:47.020
is 180
00:13:47.240 --> 00:13:48.360
times b to the 6th
00:13:49.700 --> 00:13:51.380
here comes the messy part
00:13:52.140 --> 00:13:53.020
divide by 180
00:13:54.320 --> 00:13:55.280
you get 40/180
00:13:56.440 --> 00:13:57.560
which reduces to
00:13:58.200 --> 00:13:58.700
2/9
00:14:00.240 --> 00:14:00.800
b to the 6
00:14:03.460 --> 00:14:03.960
so b
00:14:06.440 --> 00:14:06.940
is 2/9
00:14:08.760 --> 00:14:09.400
to the 1/6
00:14:10.320 --> 00:14:13.600
which you could find in your calculator, however you could just leave it to the 1/6
00:14:13.600 --> 00:14:15.600
cause thats what we expect you to do
00:14:15.600 --> 00:14:17.440
we dont expect you to figure out
00:14:17.440 --> 00:14:20.520
what that is if you cant do it without a calculator
00:14:22.180 --> 00:14:23.940
so now your equation is 180
00:14:25.080 --> 00:14:28.600
times 2/9, to the 1/6
00:14:33.780 --> 00:14:35.300
to the x or y is 180 times
00:14:36.280 --> 00:14:39.400
2/9 to the x/6, can you guys see that over there?
00:14:42.280 --> 00:14:44.040
ill rewrite that last part
00:14:50.460 --> 00:14:50.960
y
00:14:51.700 --> 00:14:52.200
is 180
00:14:53.440 --> 00:14:53.940
times
00:14:54.800 --> 00:14:55.300
2/9
00:14:56.480 --> 00:14:58.080
to the 6th, that would be
00:14:58.080 --> 00:14:59.600
and this raised to the x
00:15:00.920 --> 00:15:02.200
so thats saying 180
00:15:03.000 --> 00:15:03.500
times
00:15:03.880 --> 00:15:06.760
times 2/9, you can multiply these together
00:15:07.560 --> 00:15:08.200
to the x/6
00:15:12.160 --> 00:15:13.520
now you just plug in 1
00:15:14.980 --> 00:15:17.400
remember youre not expected to figure out what that number is
00:15:17.580 --> 00:15:18.380
we dont care
00:15:19.800 --> 00:15:20.300
2/9
00:15:22.340 --> 00:15:23.380
20/6, here we go
00:15:23.380 --> 00:15:25.800
get a calculator, you can find that exactly
00:15:26.180 --> 00:15:27.620
without a calculator
00:15:28.580 --> 00:15:30.220
i would find that exactly
00:15:30.220 --> 00:15:32.780
we have to give you nice even multiples
00:15:33.460 --> 00:15:34.740
we have to make this
00:15:38.660 --> 00:15:40.820
if i did 24 hours, it would be easy
00:15:41.220 --> 00:15:42.900
alright cause at 24 hours
00:15:44.120 --> 00:15:45.960
you would just have 24/6 is 4
00:15:47.600 --> 00:15:49.840
is 4, so you would jsut do 180 times
00:15:50.620 --> 00:15:53.420
2/9 to the 4th, its annoying but its doable
00:15:53.620 --> 00:15:57.620
but were not gonna do anything that messy, its not necessary
00:15:58.320 --> 00:16:02.160
lets do another one of these to make sure you understandit
00:16:02.760 --> 00:16:03.640
we go the idea
00:16:03.640 --> 00:16:06.440
some of you are nodding some are saying ugh
00:16:06.620 --> 00:16:07.420
seriously?
00:16:14.300 --> 00:16:14.860
alright
00:16:41.620 --> 00:16:44.500
originally you have 180 grams of an element
00:16:45.220 --> 00:16:46.980
and after 10 hours you have
00:16:48.080 --> 00:16:48.640
60 grams
00:16:48.640 --> 00:16:50.880
hhow many would you have after 30 hours?
00:16:50.880 --> 00:16:57.700
originally you have 180 grams of an element, after 10 hours its 60 grams, how many do you have after 30 hours?
00:16:58.260 --> 00:17:00.100
so you say well, originally
00:17:00.640 --> 00:17:01.680
i have 180 grams
00:17:07.180 --> 00:17:09.280
so that means i originally have the point
00:17:11.080 --> 00:17:11.580
0,180
00:17:12.000 --> 00:17:13.760
and then i would have 10,60
00:17:19.680 --> 00:17:21.280
so we figured out before
00:17:21.620 --> 00:17:22.120
so 180
00:17:24.060 --> 00:17:25.100
a times b to the 0
00:17:25.640 --> 00:17:29.080
b to the zero is one, because anyhting to the zero is 1
00:17:29.480 --> 00:17:30.200
so a is 180'
00:17:33.420 --> 00:17:36.280
so my equation can be written as 180
00:17:37.360 --> 00:17:37.860
times
00:17:38.940 --> 00:17:39.500
b to the x
00:17:40.400 --> 00:17:41.280
so far so good
00:17:45.200 --> 00:17:48.240
now that i know t equals, time equals 10 i get 60
00:17:49.180 --> 00:17:49.680
so 60
00:17:51.000 --> 00:17:51.500
is 180
00:17:52.440 --> 00:17:52.940
times b
00:17:53.860 --> 00:17:54.420
to the 10
00:17:55.880 --> 00:17:59.040
dont let the 10 scary you, thats what helps you figure out
00:17:59.140 --> 00:18:00.420
the fraction power
00:18:00.800 --> 00:18:02.720
divide by 180 and you get a 1/3
00:18:03.920 --> 00:18:04.720
is b to the 10
00:18:07.440 --> 00:18:08.080
so b is 1/3
00:18:10.300 --> 00:18:11.020
to the 1/10
00:18:17.900 --> 00:18:21.100
thats how you get the k in the denominator in the half life
00:18:21.840 --> 00:18:24.000
so that tells you that the y is 180
00:18:26.740 --> 00:18:28.100
times 1/3 to the 10th
00:18:32.540 --> 00:18:33.580
to the x, y is 180
00:18:35.220 --> 00:18:35.860
times 1/3
00:18:36.460 --> 00:18:37.420
to the x over 10
00:18:37.440 --> 00:18:39.040
couple of danger things
00:18:39.340 --> 00:18:41.660
dont multiply the 180 times the 1/3
00:18:41.700 --> 00:18:44.100
the 1/3 has to get raised to the power
00:18:45.140 --> 00:18:45.640
PEMDAS
00:18:46.160 --> 00:18:47.440
dont d 180 times 1/3
00:18:47.440 --> 00:18:49.420
thats 60, and thats not the problem
00:18:50.100 --> 00:18:53.700
only whats in the first part, we all say what the brawl?
00:18:54.040 --> 00:18:54.540
now
00:18:55.420 --> 00:18:57.260
i say how many after 30 hours
00:18:58.380 --> 00:18:59.340
so i have y=180
00:19:01.960 --> 00:19:03.000
times 1/3 to the
00:19:03.720 --> 00:19:04.220
30/10
00:19:05.360 --> 00:19:06.160
whats 30/10
00:19:07.160 --> 00:19:07.660
3
00:19:09.320 --> 00:19:10.680
so it would be y is 180
00:19:12.360 --> 00:19:13.000
times 1/3
00:19:14.120 --> 00:19:14.620
cubed
00:19:15.980 --> 00:19:17.660
and you can find 1/3 cubed
00:19:21.540 --> 00:19:22.040
ah
00:19:23.440 --> 00:19:25.680
you know how to get the x over here?
00:19:25.980 --> 00:19:28.220
so the x times the 10, thats over 10
00:19:28.220 --> 00:19:30.180
now i wanna know how many i have after 30 hours
00:19:31.320 --> 00:19:32.520
so i plug in 30 for x
00:19:43.580 --> 00:19:45.580
see why im plugging in 30 for x?
00:19:45.580 --> 00:19:48.260
cause i want to know how many i have after 30 hours
00:19:49.220 --> 00:19:51.700
so once i get to here i have my equation
00:19:51.960 --> 00:19:55.800
and then i can figure out how many i have after so many hours
00:19:58.500 --> 00:19:59.860
cause all i have to do
00:20:00.620 --> 00:20:01.580
is plug in for x
00:20:01.620 --> 00:20:03.220
and now it becomes a half
00:20:03.520 --> 00:20:04.720
so thats 100 hours
00:20:04.780 --> 00:20:05.740
i just plug in x
00:20:06.500 --> 00:20:07.060
i get 100
00:20:08.220 --> 00:20:09.980
after 17 hours, i get 17/10
00:20:12.140 --> 00:20:13.020
so the idea is
00:20:13.020 --> 00:20:15.700
by using the first 2 pieces of information
00:20:15.700 --> 00:20:17.540
i can get my general eqaution
00:20:17.540 --> 00:20:20.040
once i have that, i can get anything i want
00:20:29.940 --> 00:20:31.540
this is the final answer
00:20:31.540 --> 00:20:32.920
which you can then make
00:20:36.580 --> 00:20:37.080
180/27
00:20:44.820 --> 00:20:46.940
you can leave it like this, thats fine with me
00:20:46.940 --> 00:20:50.460
i dont think theres a difference, these are both correct
00:20:50.460 --> 00:20:52.780
you would really want to see, us to get this
00:20:52.780 --> 00:20:56.500
what we are really trying to figure out is once you figure out the formula
00:20:56.500 --> 00:21:00.360
anyone can plug in the numbers and graph, thats not the hardest part
00:21:00.360 --> 00:21:05.000
once you get to here its the easy part, the calculation is annoying but
00:21:05.000 --> 00:21:07.820
were not asking you to do the calculations were asking you to set it up
00:21:12.380 --> 00:21:15.180
okay lets have you practice one on your own
00:22:25.940 --> 00:22:26.740
try that one
00:22:35.980 --> 00:22:37.420
just like the last one
00:22:45.040 --> 00:22:47.360
first we know originally so times 0
00:22:48.620 --> 00:22:49.260
we have 24
00:22:50.720 --> 00:22:51.600
and at time 2,
00:22:52.700 --> 00:22:53.340
we have 20
00:22:55.040 --> 00:22:57.820
so we use that information and just come up with a general equation
00:23:00.960 --> 00:23:02.320
so we have 24 to start
00:23:05.940 --> 00:23:07.300
24 is a times b to the 0
00:23:07.300 --> 00:23:09.520
very small 0 if youre watching on camera
00:23:12.560 --> 00:23:14.160
and anything to the 0 is 1
00:23:16.940 --> 00:23:17.500
so 24 is a
00:23:19.600 --> 00:23:20.100
y is 24
00:23:21.300 --> 00:23:22.260
times b to the x
00:23:22.760 --> 00:23:23.960
so we can just know
00:23:24.260 --> 00:23:26.580
if we are given the starting amount
00:23:26.580 --> 00:23:27.780
the original amount
00:23:28.200 --> 00:23:29.160
thats what a is
00:23:29.880 --> 00:23:31.000
a is the starting
00:23:31.120 --> 00:23:32.960
amount, you initial amount
00:23:35.020 --> 00:23:37.180
now after 2 hours im gonna have 20
00:23:37.760 --> 00:23:38.260
20
00:23:41.100 --> 00:23:42.460
is 24 times b squared
00:23:43.680 --> 00:23:44.240
b to the 2
00:23:47.040 --> 00:23:47.840
divide by 24
00:23:48.360 --> 00:23:49.320
and you get 5/6
00:23:49.320 --> 00:23:51.400
you can certainly leave that as 20/24
00:23:52.620 --> 00:23:53.740
equals b squared
00:23:55.080 --> 00:23:55.580
so 5/6
00:23:57.120 --> 00:23:57.840
will be 1/2
00:23:57.840 --> 00:24:00.920
b. or you couldve written the square root of 5/6
00:24:00.920 --> 00:24:01.760
theyre both fine
00:24:04.580 --> 00:24:06.820
that tells us that our equation is
00:24:07.140 --> 00:24:07.640
is y
00:24:20.460 --> 00:24:20.960
so y is
00:24:24.580 --> 00:24:25.080
24
00:24:26.020 --> 00:24:26.520
times
00:24:27.760 --> 00:24:28.720
5/6 to the half
00:24:30.980 --> 00:24:31.480
times x
00:24:33.240 --> 00:24:33.740
or 24
00:24:35.700 --> 00:24:36.340
times 5/6
00:24:37.060 --> 00:24:37.700
to the x/2
00:24:39.140 --> 00:24:42.260
because you multiply x times 1/2, so you get x/2
00:24:42.740 --> 00:24:46.260
now you just need to find out how much is left at 7 hours
00:24:48.040 --> 00:24:51.200
s y=24 times 5/6
00:24:53.500 --> 00:24:54.000
7/2
00:24:55.720 --> 00:24:58.200
easy? were people able to do that one?
00:24:59.700 --> 00:25:00.500
happy? yes?
00:25:09.360 --> 00:25:12.160
i know y=a times b to the x so i plug in 24 for a
00:25:13.160 --> 00:25:15.560
now i found out that b is 5/6 to the 1/2
00:25:16.520 --> 00:25:17.160
so i take b
00:25:17.700 --> 00:25:19.700
and replace it to 5/6 to the 1/2
00:25:22.400 --> 00:25:24.400
this gets plugged in like this
00:25:27.320 --> 00:25:27.960
since 1/2
00:25:28.420 --> 00:25:31.620
to the x, i multiply the powers thats why i get x/2
00:25:31.620 --> 00:25:32.900
cause its a half of x
00:25:46.540 --> 00:25:47.900
you wouldx have this
00:25:50.200 --> 00:25:51.560
you could have that
00:25:54.860 --> 00:25:56.300
the radical is b over 2
00:25:57.220 --> 00:25:59.540
question is if you have the radical
00:25:59.660 --> 00:26:02.220
5/6, is that to the x/2 not thats to the x
00:26:02.640 --> 00:26:04.880
the radical means to the 1/2 power
00:26:08.940 --> 00:26:10.780
right and you write x to the 6
00:26:10.940 --> 00:26:11.980
so this could be
00:26:13.460 --> 00:26:13.960
24
00:26:14.240 --> 00:26:15.440
square root of 5/6
00:26:17.560 --> 00:26:18.060
to the 7
00:26:21.960 --> 00:26:23.720
how d you feel about these?
00:26:24.380 --> 00:26:25.340
loving these?
00:26:26.220 --> 00:26:28.940
why 7? i wnat to know how many after 7 hours
00:26:50.060 --> 00:26:53.180
why am i doing 1/2 times x here and then doing x/2
00:26:53.240 --> 00:26:54.140
i did that in the other one
00:26:55.280 --> 00:26:57.440
didnt i do that in previous ones?
00:26:59.920 --> 00:27:00.720
i did right?
00:27:05.740 --> 00:27:07.260
you can hate me its fine
00:28:06.240 --> 00:28:09.040
originally you have 60 grams of an element
00:28:09.440 --> 00:28:12.640
and 3 hours later you have 50 grams of the element
00:28:14.660 --> 00:28:18.420
in other words how long does it take to get down to 30 grams
00:28:26.280 --> 00:28:28.440
this is not the same, its similar
00:28:28.440 --> 00:28:30.300
you still want to set up the equation
00:28:34.340 --> 00:28:34.840
but you might
00:28:34.840 --> 00:28:36.840
might have to use logarithms
00:28:39.360 --> 00:28:40.000
might not
00:28:53.900 --> 00:28:54.700
originally
00:28:56.160 --> 00:28:57.200
theres 60 grams
00:28:57.660 --> 00:28:59.740
and 3 hours later yo have 50 gram
00:28:59.740 --> 00:29:00.920
whats the half life?
00:29:00.920 --> 00:29:02.640
couple ways you can do this
00:29:02.640 --> 00:29:04.500
and no you dont have to use logs
00:29:06.900 --> 00:29:08.420
originally you have 60
00:29:09.680 --> 00:29:11.520
and after 3 hours you have 50
00:29:12.920 --> 00:29:13.880
we want to know
00:29:15.080 --> 00:29:16.680
what time will we have 30
00:29:16.680 --> 00:29:18.520
thats what youre trying to figure out
00:29:19.240 --> 00:29:20.600
cause 30 is half of 60
00:29:23.920 --> 00:29:24.640
so we know y
00:29:26.300 --> 00:29:27.500
is a times b to the x
00:29:28.340 --> 00:29:29.060
now we know
00:29:30.100 --> 00:29:32.580
that when 0 is gonna come out 60, right
00:29:32.580 --> 00:29:34.040
everybody feel comfortable with that?
00:29:34.640 --> 00:29:35.920
thats one more time
00:29:36.620 --> 00:29:37.120
60
00:29:38.320 --> 00:29:39.520
is a times b to the 0
00:29:41.120 --> 00:29:41.620
60 is a
00:29:41.700 --> 00:29:43.460
why do i cross out b to the 0?
00:29:43.460 --> 00:29:44.840
cause anything to the 0 is 1
00:29:46.580 --> 00:29:47.620
so my first step
00:29:51.840 --> 00:29:53.120
y=60 times b to the x
00:29:55.860 --> 00:29:57.380
then i say alright well
00:29:57.600 --> 00:29:58.960
i get 50 after 3 hours
00:30:00.080 --> 00:30:00.580
so 50
00:30:02.000 --> 00:30:02.500
is 60
00:30:03.800 --> 00:30:04.840
b to the 3, cubed
00:30:08.840 --> 00:30:09.560
so i divide
00:30:10.500 --> 00:30:11.460
and you get 5/6
00:30:14.480 --> 00:30:14.980
b cubed
00:30:14.980 --> 00:30:18.060
so you can take cubed root, or you can raise it to the 1/3 power
00:30:19.300 --> 00:30:19.800
so 5
00:30:20.580 --> 00:30:21.080
6
00:30:22.240 --> 00:30:22.880
to the 1/3
00:30:23.940 --> 00:30:24.440
b
00:30:27.440 --> 00:30:28.720
now my equation is y
00:30:29.600 --> 00:30:30.100
60
00:30:30.940 --> 00:30:31.440
times
00:30:32.280 --> 00:30:32.780
5/6
00:30:34.080 --> 00:30:34.640
to the 1/3
00:30:36.600 --> 00:30:37.100
to the x
00:30:40.060 --> 00:30:40.560
or
00:30:41.700 --> 00:30:42.200
60
00:30:43.860 --> 00:30:44.500
times 5/6
00:30:46.920 --> 00:30:47.560
to the x/3
00:30:50.940 --> 00:30:51.900
so far so good?
00:30:52.200 --> 00:30:53.880
how did we do on that part?
00:30:55.300 --> 00:30:59.620
now we just have to plug in, now we have to figure out when we have 30
00:31:01.720 --> 00:31:02.220
so 30
00:31:03.100 --> 00:31:03.980
is equal to 60
00:31:05.300 --> 00:31:05.940
times 5/6
00:31:07.820 --> 00:31:08.460
to the x/3
00:31:15.120 --> 00:31:16.320
so you divide by 60
00:31:16.320 --> 00:31:17.080
and you get 1.2
00:31:17.420 --> 00:31:17.920
1/2
00:31:17.920 --> 00:31:19.040
thats the half life
00:31:20.140 --> 00:31:20.640
is 5/6
00:31:21.460 --> 00:31:24.420
to the x/3, now you want to figure out what x is
00:31:25.920 --> 00:31:27.200
we need logarithms
00:31:29.680 --> 00:31:30.940
this is why we have logarithms
00:31:39.360 --> 00:31:40.320
so far so good?
00:31:44.820 --> 00:31:46.420
okay im gonna erase this
00:31:49.760 --> 00:31:50.560
so i have 1/2
00:31:52.260 --> 00:31:52.760
is 5/6
00:31:54.480 --> 00:31:55.120
to the x/3
00:31:55.540 --> 00:31:56.980
so i take the log of 1/2
00:31:57.400 --> 00:31:58.760
i can do any log i want
00:32:03.580 --> 00:32:06.380
so basically you take the log of both sides
00:32:06.380 --> 00:32:08.140
you take the square root of both sides
00:32:08.140 --> 00:32:09.100
and square both sides
00:32:09.100 --> 00:32:10.300
take the log of both sides
00:32:11.100 --> 00:32:12.460
you like logarithms
00:32:17.900 --> 00:32:19.120
so now what do you do?
00:32:19.200 --> 00:32:20.720
make up a power in front
00:32:22.340 --> 00:32:24.100
thats why logs are so great
00:32:31.680 --> 00:32:32.320
log of 1/2
00:32:33.000 --> 00:32:33.500
is x/3
00:32:34.420 --> 00:32:34.980
log of 5/6
00:32:36.920 --> 00:32:37.960
now you can isolate x
00:32:37.960 --> 00:32:40.180
that looks scary but remember log 5/6
00:32:40.420 --> 00:32:41.300
just a number
00:32:41.300 --> 00:32:43.220
divided by a half is just some number
00:32:43.220 --> 00:32:45.260
this is what they use in chemistry by the way
00:32:48.040 --> 00:32:51.640
so what can you do? well you can multiply both sides by 3
00:32:52.440 --> 00:32:54.040
so you get 3 times the log
00:32:56.380 --> 00:32:56.880
of 1/2
00:32:57.760 --> 00:32:58.260
is
00:32:59.460 --> 00:33:00.820
x times the log of 5/6
00:33:03.280 --> 00:33:04.640
you divide by log 5/6
00:33:05.140 --> 00:33:05.700
you get 3
00:33:06.680 --> 00:33:07.180
log 1/2
00:33:09.560 --> 00:33:10.060
is log
00:33:11.880 --> 00:33:12.380
5/6
00:33:15.000 --> 00:33:15.560
equals x
00:33:21.560 --> 00:33:23.640
you can certainly take log base
00:33:25.000 --> 00:33:25.500
5/6
00:33:26.300 --> 00:33:27.740
you can do log base 5/6
00:33:28.680 --> 00:33:30.360
but thats kind of painful
00:33:31.220 --> 00:33:34.220
you could, you can also do the natural log of both sides
00:33:34.220 --> 00:33:36.280
you can do the log base whatever you want to do of both sides
00:33:39.800 --> 00:33:41.720
who was able to get to the end?
00:33:41.720 --> 00:33:44.400
not many of you, good we have to do another one then
00:33:44.900 --> 00:33:45.940
got a question?
00:33:46.040 --> 00:33:49.640
lets do one more then, ill make sure everyone gets this
00:33:50.280 --> 00:33:51.880
i got to do one more thing
00:33:54.400 --> 00:33:55.200
dont erase?
00:34:13.640 --> 00:34:16.280
i think we have a webassign due this week
00:34:16.600 --> 00:34:17.960
it wasnt posted yet?
00:34:17.960 --> 00:34:19.840
ill have to talk to professor sutherland
00:34:54.040 --> 00:34:58.600
i hope we have review in before the weekend, exams before the weekend
00:35:39.040 --> 00:35:42.000
by the way you could use the half life formula
00:35:44.280 --> 00:35:48.040
but this is just as good, it gets you in the exact same spot
00:36:34.620 --> 00:36:36.860
if you have 20 ounces of an element
00:36:36.860 --> 00:36:38.260
8 hours later you have 16 ounces
00:36:40.680 --> 00:36:42.120
what is the half life?
00:36:42.120 --> 00:36:43.520
the what i kind of erased there
00:36:47.240 --> 00:36:48.600
so at time 0 we have 20
00:36:50.600 --> 00:36:51.400
and at time 8
00:36:51.860 --> 00:36:52.820
were down to 16
00:36:54.040 --> 00:36:54.600
so time x
00:36:55.060 --> 00:36:56.740
your gonna need to have 10
00:37:02.480 --> 00:37:04.320
so we know y=a times b to the x
00:37:05.260 --> 00:37:06.060
and you know
00:37:07.720 --> 00:37:08.440
at 0 we get a
00:37:10.000 --> 00:37:10.960
so this is y=20
00:37:12.640 --> 00:37:13.200
b to the x
00:37:14.300 --> 00:37:14.800
now
00:37:15.780 --> 00:37:18.020
i need to figure out the other part
00:37:18.480 --> 00:37:20.160
i plug in 8 for x and i get 16
00:37:20.480 --> 00:37:20.980
for y
00:37:22.940 --> 00:37:23.580
so i ahd 16
00:37:25.660 --> 00:37:26.160
is 20
00:37:28.180 --> 00:37:28.680
to the 8
00:37:32.180 --> 00:37:32.980
16/20 is 4/5
00:37:35.080 --> 00:37:36.680
or you can leave it 16/20
00:37:40.000 --> 00:37:40.500
b
00:37:41.700 --> 00:37:42.200
is 4/5
00:37:44.140 --> 00:37:44.780
to the 1/8
00:37:46.920 --> 00:37:47.880
so far so good?
00:37:49.720 --> 00:37:50.220
so y
00:37:51.440 --> 00:37:51.940
is 20
00:37:53.780 --> 00:37:54.420
times 4/5
00:37:56.220 --> 00:37:56.860
to the x/8
00:37:59.680 --> 00:38:00.480
doing okay?
00:38:01.220 --> 00:38:03.700
doing alright? getting good grades?
00:38:16.940 --> 00:38:18.620
i need to know wheni get 10
00:38:27.320 --> 00:38:32.040
and we gonna divide 10 by 20 and get 1/2, were trying to find the half life
00:38:33.120 --> 00:38:34.000
so this is 4/5
00:38:36.340 --> 00:38:36.980
to the x/8
00:38:37.120 --> 00:38:38.800
when you have an equation
00:38:39.420 --> 00:38:40.300
and you have x
00:38:40.900 --> 00:38:43.380
in the power so you dont know the power
00:38:43.800 --> 00:38:45.800
thats when you use logarithms
00:38:46.000 --> 00:38:47.920
you take the log of both sides
00:38:58.180 --> 00:39:00.900
and now thanks to the power of logarithms
00:39:00.900 --> 00:39:02.980
you can bring the x over, right in front
00:39:03.760 --> 00:39:04.480
and you get
00:39:05.640 --> 00:39:06.280
log of 1/2
00:39:08.020 --> 00:39:08.520
is x/8
00:39:10.480 --> 00:39:11.120
log of 4/5
00:39:16.500 --> 00:39:18.340
now multiply both sides by 8
00:39:28.320 --> 00:39:29.680
and divide by log 4/5
00:39:35.680 --> 00:39:42.680
and you leave it like that, in fact you should leave it like that because you dont know what log 1/2 divided by log 4/5 is
00:39:42.840 --> 00:39:44.680
you put that in a calculator
00:39:48.600 --> 00:39:49.560
so far so good?
00:39:52.320 --> 00:39:53.120
questions?
00:39:55.800 --> 00:39:57.560
where does the 8 come from?
00:40:00.420 --> 00:40:01.140
we have x/8
00:40:01.140 --> 00:40:02.980
thats in the denominator so you have x
00:40:03.880 --> 00:40:05.000
times the log 4/5
00:40:05.420 --> 00:40:06.220
divided by 8
00:40:06.220 --> 00:40:08.120
so you multiply both sides by 8
00:40:08.500 --> 00:40:10.580
not you just have x times log 4/5
00:40:12.920 --> 00:40:15.240
now the log of this is just a decimal
00:40:15.420 --> 00:40:16.700
thats just a number
00:40:16.700 --> 00:40:19.100
log of 1/2 is just a number, so you have 8
00:40:19.100 --> 00:40:21.240
times some number divided by some other number
00:40:21.240 --> 00:40:23.460
if you were doing this with a calculator
00:40:23.460 --> 00:40:25.380
you could figure these out first
00:40:26.940 --> 00:40:28.700
you can do 8 times log of 1/2
00:40:28.700 --> 00:40:31.080
equals x times something, divided by something
00:40:31.080 --> 00:40:32.760
but since you dont have a caslcultaor
00:40:32.760 --> 00:40:35.080
you have to get it down to that point
00:40:39.400 --> 00:40:40.900
lets do a couple other things with logarithms
00:40:52.080 --> 00:40:53.760
so0 remeber the log laws?
00:40:55.060 --> 00:40:58.500
right them down, i think i put them up.. i posted them
00:40:59.960 --> 00:41:01.000
theres3 of them
00:41:02.540 --> 00:41:03.740
the log of a times b
00:41:05.600 --> 00:41:06.400
equals log a
00:41:08.260 --> 00:41:08.900
plus log b
00:41:13.900 --> 00:41:15.740
you have log of a divided by b
00:41:18.240 --> 00:41:21.220
log a minus log b
00:41:23.600 --> 00:41:24.320
and log of a
00:41:24.520 --> 00:41:26.840
to the b, this is the one we just used
00:41:28.760 --> 00:41:29.260
b times
00:41:30.940 --> 00:41:31.660
the log of a
00:41:31.660 --> 00:41:33.360
thats the most important one
00:41:33.360 --> 00:41:35.200
for those kind of equations we just did
00:41:35.760 --> 00:41:36.400
that says
00:41:38.680 --> 00:41:41.960
that if you have log of something raised to a power
00:41:41.960 --> 00:41:43.620
you can bring the power in front
00:41:55.000 --> 00:41:56.040
so what if i said
00:41:56.040 --> 00:41:58.340
i wanted you just to take something like
00:42:01.320 --> 00:42:06.040
i wanted to break that apart, remember using logarithms in high scool?
00:42:09.700 --> 00:42:11.380
i have the log of x squared
00:42:11.380 --> 00:42:14.020
y cubed, thats the two things multiplied together
00:42:14.980 --> 00:42:17.220
so i can make that a log of x squared
00:42:20.300 --> 00:42:21.740
plus the log of y cubed
00:42:23.360 --> 00:42:25.440
this is very useful in calculus
00:42:25.440 --> 00:42:27.820
when you do something thats called logarithm differentiation
00:42:28.760 --> 00:42:29.800
very fancy word
00:42:29.800 --> 00:42:32.480
for something thats actually very helpful
00:42:39.020 --> 00:42:41.100
now i can break this up even more
00:42:41.100 --> 00:42:42.660
because log x squared is
00:42:42.960 --> 00:42:44.160
2 times the log of x
00:42:47.080 --> 00:42:48.440
and log of y cubed is 3
00:42:49.680 --> 00:42:50.800
times the log of y
00:42:59.780 --> 00:43:01.540
what if i wanted to break up
00:43:10.860 --> 00:43:12.540
log x to the 3 over y to the 5
00:43:24.940 --> 00:43:27.900
well log x to the 3 over y to the 5 is log x to the 3
00:43:31.380 --> 00:43:32.580
minus log y to the 5
00:43:36.320 --> 00:43:39.280
and i can take the powers and put them in front
00:43:40.880 --> 00:43:42.240
i can say this is 3 log
00:43:43.040 --> 00:43:44.840
x minus 5
00:43:46.900 --> 00:43:47.400
log y
00:43:48.580 --> 00:43:50.340
so this is breaking up a log
00:43:50.740 --> 00:43:52.340
its very useful because
00:43:52.340 --> 00:43:56.100
you dont as much trouble as working in this form as you do working in this form
00:43:57.000 --> 00:43:59.040
first you have to be spectacle of both directions
00:44:03.600 --> 00:44:07.600
i give you some time to copy this down before i erase the board
00:44:39.120 --> 00:44:41.280
what if i wanted to break that up?
00:44:41.980 --> 00:44:43.180
lets break this up
00:44:44.700 --> 00:44:46.140
we can make this log of
00:44:47.420 --> 00:44:47.980
x to the 4
00:44:48.980 --> 00:44:50.420
square root of y minus
00:44:52.220 --> 00:44:53.340
log of z squared\
00:44:55.760 --> 00:44:56.640
so far so good
00:44:58.500 --> 00:45:01.140
so log x to the 4 times the square root of y
00:45:01.140 --> 00:45:03.240
is two things multiplied together
00:45:03.740 --> 00:45:05.340
so i can make that lof of x
00:45:05.600 --> 00:45:06.100
to the 4
00:45:06.400 --> 00:45:06.900
plus
00:45:07.800 --> 00:45:09.080
log square root of y
00:45:09.900 --> 00:45:10.400
minus
00:45:13.140 --> 00:45:14.180
log of z squared
00:45:18.200 --> 00:45:20.280
now i can put the powers in front
00:45:21.780 --> 00:45:22.280
4 log x
00:45:23.220 --> 00:45:25.940
square root of y is the same as what power?
00:45:27.060 --> 00:45:27.560
1/2
00:45:28.140 --> 00:45:29.180
thats a 1/2 log y
00:45:32.020 --> 00:45:32.520
minus
00:45:34.360 --> 00:45:34.860
2 log z
00:45:38.420 --> 00:45:39.940
howd you do on this one?
00:45:41.380 --> 00:45:42.340
so far so good?
00:45:43.500 --> 00:45:45.500
now were gonna go the other way
00:45:46.620 --> 00:45:49.340
ill wait till everybody copied this down
00:45:55.780 --> 00:45:57.860
square root of y is the 1/2 power
00:46:00.600 --> 00:46:02.920
so its the same as saying y to the 1/2
00:46:04.160 --> 00:46:05.760
so thats why its 1/2 log y
00:46:11.580 --> 00:46:13.260
im losing a lot of you guys
00:46:13.260 --> 00:46:15.140
hang in there you only have a few more minutes
00:46:16.320 --> 00:46:18.240
okay so im gonna cover this up
00:46:40.260 --> 00:46:42.260
okay right that as a single log
00:46:42.480 --> 00:46:44.480
this becomes the log of x cubed
00:46:47.200 --> 00:46:49.360
this becomes the log of y squared
00:46:51.920 --> 00:46:53.680
and that becomes the log of
00:46:55.620 --> 00:46:56.180
z to the 4
00:47:03.240 --> 00:47:06.200
now we have log of x cubed plus log of y squared
00:47:06.760 --> 00:47:09.480
thats the log of x cubed times log squared
00:47:11.140 --> 00:47:12.660
and i got minus z to the 4
00:47:14.200 --> 00:47:16.520
so z to the 4 goes in the denominator
00:47:22.960 --> 00:47:23.760
one last one
00:47:25.440 --> 00:47:27.680
make sure you guys get the concept
00:47:29.600 --> 00:47:30.480
what if i said
00:47:31.600 --> 00:47:32.100
i wrote
00:47:41.820 --> 00:47:42.940
what if i had that
00:47:44.220 --> 00:47:47.980
this is the one that tends to mess people up but t shouldnt
00:47:50.540 --> 00:47:51.040
4 log x
00:47:52.840 --> 00:47:54.680
is still log x to the 4 right?
00:48:01.620 --> 00:48:03.540
2 log y, is still log y squared
00:48:08.040 --> 00:48:09.720
3 log z is still log z cubed
00:48:17.020 --> 00:48:19.180
this becomes log of, heres where
00:48:20.060 --> 00:48:21.660
heres where we mess it up
00:48:32.880 --> 00:48:35.040
thats where everybody messes up
00:48:37.340 --> 00:48:43.020
just because i have this one minus this one plus this one, doesnt make it any different
00:48:43.160 --> 00:48:44.760
that it would be this way
00:48:46.560 --> 00:48:49.280
so basically everything that i am adding
00:48:50.120 --> 00:48:51.720
goes into the numerator
00:48:51.720 --> 00:48:53.160
and everything that im subtracting
00:48:54.180 --> 00:48:55.940
goes into the denominator
00:48:56.280 --> 00:48:58.760
doesnt matter where i put them right?
00:49:00.580 --> 00:49:01.540
a minus b plus c
00:49:02.180 --> 00:49:04.340
is the same thing a a plus c minus b