91Ó°ÊÓ

An artifact originally had 16 grams of carbon- 14 present. The decay model \(A=16 e^{-0.0001211}\) describes the amount of carbonI 4 present, \(A,\) in grams, after \(t\) years. How many grams of carbon-14 will be present after \(11,430\) years?

Solve each exponential equation in Exercises \(1-26\) Express the solution set in terms of natural logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$e^{4 x-5}-7=11,243$$

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. \(g(x)=\left(\frac{4}{3}\right)^{x}\)

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. \(h(x)=\left(\frac{1}{2}\right)^{x}\)

Solve each exponential equation in Exercises \(1-26\) Express the solution set in terms of natural logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$7^{x+2}=410$$

Write each equation in its equivalent logarithmic form. $$13^{2}=x$$

In Exercises \(1-40,\) use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$ \log _{b} x^{3} $$

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. \(h(x)=\left(\frac{1}{3}\right)^{x}\)

In Exercises \(1-40,\) use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$ \log _{b} x^{7} $$

Write each equation in its equivalent logarithmic form. $$15^{2}=x$$