Mathematics 133 – Intensive Calculus for Science 1 Exam I – September 28, 2001

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

\begin{matrix}x = & 0 & 0.1 & 0.2 & 0.3 & 0.4 \\ f(x) = & −4.2 & −5.9 & −7.6 & −9.3 & −11.0 \\ g(x) = & 10 & 20 & 40 & 80 & 160 \\ h(x) = & 4 & 2.3 & 1.5 & 2.1 & 6.1 \end{matrix}

A) (10) One of these is a linear function. Explain how you can tell which one it is, and

give formula for it. B) (10) One of these functions is neither linear nor exponential. Which one is it and

why?

II. (20) The population of a colony of bacteria at time t (in hours) is growing at a continuous rate of .12% per hour. Will the population ever equal 10000? If so, when does that happen? (leave your answer in “exact” form).

III. (20) Solve for x: 15^{2x+3} = 5 · 2^{x}.

IV. Consider the following two graphs and assume that the whole domain is shown in both plots.

A) (10) One of the two functions has an inverse function. Say which one it is and give a

rough sketch of the graph of the inverse function of that one. B) (10) Find a possible formula for the other one.

V. True or false: A) (10) The following graph could be the graph of a polynomial function of degree 5.

Explain your answer.

B) (10) The following graph shows y = \frac{x}{x^{2}−1}. Explain your answer.