* This is an 90-minute test. Work all questions. You may use a
programmable, graphing
calculator. ***
As usual, no credit for
unexplained work!**

** 1.**
Three functions of *x* are tabulated below (the values are rounded
off to three decimal places). One is linear
(of the form *mx*+*b*), one is exponential (of the form
*C*e^(*kx*)) and one is
quadratic (of the form *ax*^2+*bx*+*c*).
Which is which? Explain your
answers.

xf(x)g(x)h(x) 1.1 6.400 7.050 6.340 1.2 5.328 5.875 5.423 1.3 4.335 4.896 4.506 1.4 3.362 4.080 3.589 1.5 2.409 3.400 2.672

** b.** Use your calculator to determine the value of
*g*(0.55) to 2 decimal
places.

** 3.**
A cup of hot coffee left in a cool room will get colder. If the room
temperature is 20 degrees C, and the cup starts off at 100 degrees C,
Newton's Law of Cooling implies that the temperature *H* of the coffee,
in degrees Centigrade, as a function of time *t* in minutes will be

*H*(*t*) = 20 + 80 e^{-*kt*}

for some *k* > 0.

** a.** Suppose that after 12 minutes the coffee has cooled to
60 degrees C. Use this information to calculate *k*.

** b.** How long will it take the coffee to cool to 40 degrees C?
Show your work!

** c.** Sketch the graph of *H*(*t*). Pay careful attention to
the initial value *H*(0), the limiting value as *t* --> \infty,
the slope and the concavity of your graph.

** 4.**
The position of an object falling vertically through air was recorded every
1/10 second; part of the record is shown in this table:

time (seconds 13.1 13.2 13.3 13.4 13.5 height(cm.) 529.67 423.10 307.83 183.95 51.54

** a.**
Estimate the instantaneous velocity of this object at 13.4 seconds.
Show your work.

** b.** Estimate the acceleration of this object at 13.4 seconds.
Show your work.