91Ó°ÊÓ

Exercises \(45-52\) involve equations with natural logarithms. Solve each equation by isolating the natural logarithm and exponentiating both sides. Express the answer in terms of \(e\) Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$6+2 \ln x=5$$

Use the formula \(R=6 e^{12.77 x},\) where \(x\) is the blood alcohol concentration and \(R,\) given as a percent, is the risk of having a car accident, to solve Exercises \(53-54\) What blood alcohol concentration corresponds to a \(50 \%\) risk of a car accident?

The formula \(A=18.9 e^{0.0055 t}\) models the population of New York State, \(A\), in millions, \(t\) years after 2000 . a. What was the population of New York in \(2000 ?\) b. When will the population of New York reach 19.6 million?

The \(p H\) of a solution ranges from 0 to \(14 .\) An acid solution has a pH less than 7. Pure water is neutral and has a pH of 7. Normal, unpolluted rain has a p \(H\) of about \(5.6 .\) The pH of a solution is given by $$ \mathrm{pH}=-\log x $$ where \(x\) represents the concentration of the hydrogen ions in the solution, in moles per liter. Use the formula to solve Exercises \(69-70\) The figure shows very acidic rain in the northeast United States. What is the hydrogen ion concentration of rainfall with a pH of \(4.2 ?\) Express the answer as a power of \(10,\) and then round to the nearest hundredthousandth.

In Exercises \(79-82,\) use a graphing utility and the change-of- base property to graph each function.$$ y=\log _{15} x $$