91Ó°ÊÓ

Use the exponential decay model for carbon- \(14, A=A_{0} e^{-0.000121 t}\) Prehistoric cave paintings were discovered in a cave in France. The paint contained \(15 \%\) of the original carbon- \(14 .\) Estimate the age of the paintings.

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible,evaluate logarithmic expressions without using a calculator. $$\ln \sqrt[5]{x}$$

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$8^{x+3}=16^{x-1}$$

write each equation in its equivalent logarithmic form. $$7^{y}=200$$

Use the exponential decay model for carbon- \(14, A=A_{0} e^{-0.000121 t}\) Skeletons were found at a construction site in San Francisco in \(1989 .\) The skeletons contained \(88 \%\) of the expected amount of carbon-14 found in a living person. In \(1989,\) how old were the skeletons?

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$8^{1-x}=4^{x+2}$$

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible,evaluate logarithmic expressions without using a calculator. $$\ln \sqrt[7]{x}$$

write each equation in its equivalent logarithmic form. $$8^{y}=300$$

evaluate each expression $$\log _{4} 16$$

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$e^{x+1}=\frac{1}{e}$$