91Ó°ÊÓ

State which of the following models might be appropriate for the given scatter plot of data (more than one model may be appropriate $$\begin{array}{|l|l|} \hline \m{}{|c|}\text { Model } & \text { Corresponding Function } \\ \hline \text { A. Linear } & y=a x+b \\ \hline \text { B. Quadratic } & y=a x^{2}+b x+c \\ \hline \text { C. Power } & y=a x^{r} \\ \hline \text { D. Cubic } & y=a x^{3}+b x^{2}+c x+d \\ \hline \text { E. Exponential } & y=a b^{x} \\ \hline \text { F. Logarithmic } & y=a+b \ln x \\ \hline \text { G. Logistic } & y=\frac{a}{1+b e^{-k x}} \\ \hline \end{array}$$ (GRAPH CAN NOT COPY)

Find the logarithm, without using a calculator. $$\log .001$$

Sketch a complete graph of the function. $$f(x)=(1.001)^{-x}$$

Compute the ratios of successive entries in the table to determine whether or not an exponential model is appropriate for the data. $$\begin{array}{|l|l|l|l|l|l|l|} \hline x & 1 & 3 & 5 & 7 & 9 & 11 \\ \hline y & 3 & 21 & 55 & 105 & 171 & 253 \\ \hline \end{array}$$

Use the Big-Little Principle to explain why \(e^{x}+e^{-x}\) is approximately equal to \(e^{x}\) when \(x\) is large.

Write the given expression without using radicals. $$\sqrt[5]{x^{2}}$$

The table gives the death rate in motor vehicle accidents (per 100,000 population) in selected years. $$\begin{array}{|l|c|c|c|c|c|c|c|} \hline \text { Year } & 1970 & 1980 & 1985 & 1990 & 1995 & 2000 & 2003 \\ \hline \text { Death Rate } & 26.8 & 23.4 & 19.3 & 18.8 & 16.5 & 15.6 & 15.4 \\\ \hline \end{array}$$ (a) Find an exponential model for the data, with \(x=0\) corresponding to 1970 . (b) What was the death rate in 1998 and in \(2002 ?\) (c) Assume that the model remains accurate, when will the death rate drop to 13 per \(100,000 ?\)

(a) Solve \(7^{x}=3,\) using natural logarithms. Leave your answer in logarithmic form; don't approximate with a calculator. (b) Solve \(7^{x}=3,\) using common (base 10 ) logarithms. Leave your answer in logarithmic form. (c) Use the change of base formula in Special Topics \(5.4 . \mathrm{A}\) to show that your answers in parts (a) and (b) are the same.

Rationalize the denominator and simplify your answer. $$\frac{1+\sqrt{3}}{5+\sqrt{10}}$$

Rationalize the denominator and simplify your answer. $$\frac{10}{\sqrt[3]{2}}$$