91Ó°ÊÓ

Graph each function. Determine whether each function is an increasing or a decreasing function. See Objective 5. $$ y=\log _{1 / 2} x $$

Cross Country Skiing. The function \(H(s)=-47.73+107.38\) ln \(s\) approximates the heart rate (in beats/minute) for an Olympic-class cross country skier traveling at \(s\) miles per hour, where \(s>5\) mph. Find the heart rate of a skier traveling at a rate of 7.5 miles per hour.

Graph each function. Determine whether each function is an increasing or a decreasing function. See Objective 5. $$ y=\log _{4} x $$

The half-life of tritium is 12.4 years. How long will it take for \(25 \%\) of a sample of tritium to decompose?

Which pair of expressions in each list are equivalent? a. \(\log (9 \cdot 3)\) b. \(\log 9 \cdot \log 3\) c. \(\log 9+\log 3\)

Maturity Levels. The function \(P(a)=41.0+20.4 \ln a\) approximates the percent of adult height attained by an earlymaturing girl of age \(a\) years, for \(1 \leq a \leq 18 .\) The function \(P(a)=37.5+20.2 \ln a\) does the same for a late-maturing girl. Find the difference in percent of their adult height for both maturity types on their 10 th birthday.

In 2 years, \(20 \%\) of a radioactive element decays. Find its half-life.

Which pair of expressions in each list are equivalent? a. \(\log _{6} \frac{7}{9}\) b. \(\frac{\log _{6} 7}{\log _{6} 9}\) c. \(\log _{6} 7-\log _{6} 9\)

An isotope of thorium, written as 227 Th, has a half-life of 18.4 days. How long will it take for \(80 \%\) of the sample to decompose?

Explain why the graph of \(y=e^{x}-5\) is five units below the \(\operatorname{graph}\) of \(y=e^{x}\)