91Ó°ÊÓ

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. $$5^{x}=17$$

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 lead is 22 years. How long will it take for a sample of this substance to decay to \(80 \%\) of its original amount?

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. $$9 e^{x}=107$$

evaluate each expression $$\log _{5} 5$$

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. $$e^{4 x-5}-7=11,243$$

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 $$ f(x)=\frac{12.57}{1+4.11 e^{-0.026 x}} $$ How well does the function model the data showing a world population of 6.1 billion for \(2000 ?\)

Graph \(f(x)=4^{x}\) and \(g(x)=\log _{4} x\) in the same rectangular coordinate system.

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. $$\ln x+\ln 7$$

Use Newton's Law of Cooling, \(T=C+\left(T_{0}-C\right) e^{k t},\) to solve Exercises \(47-50\). A bottle of juice initially has a temperature of \(70^{\circ} \mathrm{F}\). It is left to cool in a refrigerator that has a temperature of \(45^{\circ} \mathrm{F}\). After 10 minutes, the temperature of the juice is \(55^{\circ} \mathrm{F}\) a. Use Newton's Law of Cooling to find a model for the temperature of the juice, \(T\), after \(t\) minutes. b. What is the temperature of the juice after 15 minutes? c. When will the temperature of the juice be \(50^{\circ} \mathrm{F} ?\)

Use Newton's Law of Cooling, \(T=C+\left(T_{0}-C\right) e^{k t},\) to solve Exercises \(47-50\). A pizza removed from the oven has a temperature of \(450^{\circ} \mathrm{F}\) It is left sitting in a room that has a temperature of \(70^{\circ} \mathrm{F}\). After 5 minutes, the temperature of the pizza is \(300^{\circ} \mathrm{F}\) a. Use Newton's Law of Cooling to find a model for the temperature of the pizza, \(T\), after \(t\) minutes. b. What is the temperature of the pizza after 20 minutes? c. When will the temperature of the pizza be \(140^{\circ} \mathrm{F} ?\)