Mathematics 133 – Intensive Calculus for Science 1 Sample Exam I – September 21, 2001

Directions : Do all work in the blue exam booklet. You may use a calculator on any of the following problems. There are 100 possible points, distributed as indicated.

I. The following table contains values for three different functions: f(x), g(x), h(x).

\begin{matrix}x = & −2 & 0 & 2 & 4 & 6 \\ f(x) = & −2.1 & 0 & 3.4 & 2.3 & 1.1 \\ g(x) = & 23.1 & 25.3 & 27.5 & 29.7 & 31.9 \\ h(x) = & 10.67 & 26.67 & 66.67 & 166.67 & 416.67 \end{matrix}

A) (10) Which (if any) of these are linear functions? For those that are linear give a

formula. B) (10) Which (if any) of these are (approximately) exponential functions? For those

that are approximately exponential, give a formula.

II. (20) A radioactive element has a half-life of 12 years. If 10 oz. are present originally in a sample, how long will it take for the amount to decay to 1 oz.?

III. (15) The following graph shows y = f(x). Copy this graph in your exam booklet, and on the same axes, sketch y = 3f(x + 1) − 1.

IV. (15) Solve for x: e^{−5x} = 10^{x+2}.

V. (15) Find a possible formula for the following function.

VI. (15) Suppose that Q(t) with domain 0 ≤ t < 24 (time in hours) is the temperature in Worcester as a function of time on a typical day in September. Would you expect Q to have an inverse function? If so, say what the equation Q^{−1}(65) = 11 means. If not, say why not.