91Ó°ÊÓ

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. $$ 125^{x}=625 $$

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$ \log _{b} x^{7} $$

The half-life of the radioactive element krypton-91 is 10 seconds. If 16 grams of krypton- 91 are initially present, how many grams are present after 10 seconds? 20 seconds? 30 seconds? 40 seconds? 50 seconds?

In Exercises 21–42, evaluate each expression without using a calculator. $$ \log _{7} 49 $$

In Exercises 21–42, evaluate each expression without using a calculator. $$ \log _{5} \frac{1}{5} $$

In Exercises 21–42, evaluate each expression without using a calculator. $$ \log _{6} \frac{1}{6} $$

Use the exponential decay model, \(A=A_{0} e^{k t},\) to solve Exercises \(28-31 .\) Round answers to one decimal place. The half-life of aspirin in your bloodstream is 12 hours. How long will it take for the aspirin to decay to \(70 \%\) of the original dosage?

Shown, again, in the following table is world population, in billions, for seven selected years from 1950 through \(2010 .\) Using a graphing utility's logistic regression option, we obtain the equation shown on the screen. $$ \begin{array}{cc} {x, \text { Number of Years }} & {y, \text { World Population }} \\ {\text { after } 1949} & {\text { (billions) }} \\ {1(1950)} & {2.6} \\ {11(1960)} & {3.0} \\ {21(1970)} & {3.7} \\ {21(1970)} & {4.5} \\ {41(1990)} & {5.3} \\ {51(2000)} & {6.1} \\ {61(2010)} & {6.9} \end{array} $$ We see from the calculator screen at the bottom of the previous page that a logistic growth model for world population, \(f(x),\) in billions, \(x\) years after 1949 is $$ f(x)=\frac{12.57}{1+4.11 e^{-0.026 x}} $$ Use this function to solve Exercises \(38-42\) How well does the function model the data showing a world population of 6.9 billion for \(2010 ?\)

Use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is \(1 .\) Where possible, evaluate logarithmic expressions without using a calculator. $$ \log 5+\log 2 $$