91Ó°ÊÓ

Approximate each number using a calculator. Round your answer to three decimal places. $$2^{3.4}$$

The exponential models describe the population of the indicated country, \(A,\) in millions, t years after \(2010 .\) Use these models to solve Exercises \(1-6\). \begin{aligned} &\text { India } \quad A=1173.1 e^{0.008 t}\\\ &\text { Iraq } \quad A=31.5 e^{0.019 t}\\\ &\text { Japan } \quad A=127.3 e^{-0.006 t}\\\ &\text { Russia } \quad A=141.9 e^{-0.005 t} \end{aligned} Which countries have a decreasing population? By what percentage is the population of these countries decreasing each year?

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$5^{x}=625$$

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$32^{x}=8$$

In Exercises \(11-18\), graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. $$f(x)=4^{x}$$

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$5^{2-x}=\frac{1}{125}$$

The half-life of the radioactive element plutonium-239 is \(25,000\) years. If 16 grams of plutonium- 239 are initially present, how many grams are present after \(25,000\) years? \(50,000\) years? \(75,000\) years? \(100,000\) years? \(125,000\) years?

write each equation in its equivalent logarithmic form. $$b^{3}=343$$

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. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$5^{x}=17$$