91Ó°ÊÓ

Find \(f(x)\) and \(g(x)\) such that \(h(x)=(f \circ g)(x) .\) Answers may vary. $$ h(x)=(x-9)^{3} $$

The Louisiana Purchase. In \(1803,\) the United States negotiated the Louisiana Purchase with France. The country doubled its territory by adding \(827,000\) square miles of land for \(\$ 15\) million. If the land appreciated at the rate of \(6 \%\) each year, what would one square mile of land be worth in \(2005 ?\)

Solve each equation. See Example \(9 .\) $$ \log 5-\log x=1 $$

Find the inverse of each function. Then graph the function and its inverse on one coordinate system. Show the line of symmetry on the graph. \(f(x)=2 x\)

Solve for \(x\). See Example 3 . $$ \log _{x} 0.001=-3 $$

Solve each equation. Give the exact solution and, when appropriate, an approximation to four decimal places. $$ 7^{x^{2}}=10 $$

Write logarithm as the sum and/or difference of logarithms of a single quantity. Then simplify, if possible. \(\log _{a} \frac{\sqrt[3]{x}}{\sqrt[4]{y z}}\)

How does exponential growth differ from linear growth? Give an example.

assume that there are no deposits or withdrawals. Continuous Compound Interest. An initial investment of \(\$ 2,000\) earns \(8 \%\) interest, compounded continuously. What will the investment be worth in 15 years?

assume that there are no deposits or withdrawals. Determining the Initial Deposit. \(\quad\) An account now contains \(\$ 11,180\) and has been accumulating interest at \(7 \%\) annual interest, compounded continuously, for 7 years. Find the initial deposit.