Mathematics 133 – Intensive Calculus for Science 1 Exam I – September 28, 2005

Directions: Do all work in the blue exam booklet. There are 100 possible points, distributed as indicated before the questions – (10) means the question is worth 10 points for instance. No calculators on this exam.

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) & 1 & 0 & 3 & 2 & 1 \\ g(x) & 23 & 28 & 33 & 38 & 43 \\ h(x) & 18 & 2 & 2/9 & 2/81 & 2/729 \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 exponential functions? For those that are exponential,

give a formula.

II. (20) The radioactive element Explosium^{224} decays exponentially with a half-life of 12 years. If 10 g are present originally in a sample, how long will it take for the amount to decay to 1 g? (Leave your answer in “exact form”.)

III. (30) The back of this sheet shows two plots A and B. Find possible formulas for the two functions and explain how you determined your results.

IV. (15) Does the function f(x) = 10^{x+1} have an inverse function? If so, say why and find a formula for the inverse function. If not, say why not.

V. (15) All parts of this question refer to the rational function

r(x) = \frac{2x^{2} − x}{16 − x^{2}}.

A) (5) Where does the graph of r(x) have vertical asymptotes? B) (5) Where does the graph have a horizontal asymptote? C) (5) Where does the graph of r(x) cross the x-axis?