91Ó°ÊÓ

Computer Viruses. Suppose the number of computers infected by the spread of a virus through an e-mail is described by the exponential function \(c(t)=5(1.034)^{t},\) where \(t\) is the number of minutes since the first infected e-mail was opened. a. Graph the function. Scale the \(t\) -axis from 0 to \(400,\) in units of \(50 .\) Scale the \(c(t)\) -axis from 0 to \(800,000\) in units of \(100,000\) b. Use the function to determine the number of infected computers in 8 hours, which is 480 minutes.

Write each logarithm as the sum and/or difference of logarithms of a single quantity. Then simplify, if possible. See Example 4. $$ \log \frac{7 c}{2} $$

Evaluate each expression without using a calculator. $$ \ln e^{6} $$

The function \(P(t)=35.8(1.06)^{t}\) approximates the number of people (in millions) in the United States living in poverty, where \(t\) is the number of years after \(2006 .\) Use the function to complete the table below. Round to the nearest tenth. (Source: U.S. Census Bureau) $$ \begin{array}{|l|l|l|l|l|} \hline \text { Year } & 2006 & 2007 & 2008 & 2009 \\ \hline \begin{array}{l} \text { Number in poverty } \\ \text { (in millions) } \end{array} & & & & \\ \hline \end{array} $$

Write each logarithm without an exponent or a radical symbol. Then simplify, if possible. See Example \(5 .\) $$ \ln z^{9} $$

Write each logarithm without an exponent or a radical symbol. Then simplify, if possible. See Example \(5 .\) $$ \log \sqrt[3]{7} $$

Find \(f(x)\) and \(g(x)\) such that \(h(x)=(f \circ g)(x) .\) Answers may vary. See Example 5. $$ h(x)=\frac{1}{x-4} $$

Solve each equation. $$ \log _{5}(4 x-1)+\log _{5} x=1 $$

Show that each pair of functions are inverses. $$ f(x)=2 x+9, f^{-1}(x)=\frac{x-9}{2} $$

Solve for \(x .\) See Example 3. $$ \log _{3} x=-4 $$