91Ó°ÊÓ

If $$\$ 1$$ is invested in an account over a 10 -year period, the amount in the account, where \(t\) represents the time in years, is given by $$ A=1+0.06 \llbracket t \rrbracket \quad \text { or } \quad A=\left(1+\frac{0.055}{365}\right)^{\llbracket 365 t \rrbracket} $$ depending on whether the account pays simple interest at \(6 \%\) or compound interest at \(5 \frac{1}{2} \%\) compounded daily. Use a graphing utility to graph each function in the same viewing window. Which grows at a higher rate?

In Exercises 23-26, use a graphing utility to graph the exponential function. $$ y=3^{-|x|} $$

\(x=\frac{1}{500}\)

In Exercises 23-26, use a graphing utility to graph the exponential function. $$ y=3^{x-2}+1 $$

Find the exact value of the logarithmic expression without using a calculator. (If this is not possible, state the reason.) \(\log _{2} \sqrt[4]{8}\)

In Exercises 25-66, solve the exponential equation algebraically. Approximate the result to three decimal places. $$ e^{x}=e^{x^{2}-2} $$

Radioactive Decay In Exercises 25-30, complete the table for the radioactive isotope. \(\begin{array}{cccc} & \text { Half-life } & \text { Initial } & \text { Amount After } \\ \text { Isotope } & \text { (years) } & \text { Quantity } & 1000 \text { Years }\end{array}\) $$ { }^{226} \mathrm{Ra} \quad 1599 \quad 10 \mathrm{~g} $$

In Exercises 25-66, solve the exponential equation algebraically. Approximate the result to three decimal places. $$ e^{2 x}=e^{x^{2}-8} $$

In Exercises 23-26, use a graphing utility to graph the exponential function. $$ y=4^{x+1}-2 $$

Find the exact value of the logarithmic expression without using a calculator. (If this is not possible, state the reason.) \(\log _{6} \sqrt[3]{6}\)