91Ó°ÊÓ

Tritium Decay. 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. \(\log 9+\log 3\)

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. (Source: Growth, Maturation, and Physical Activity, Human Kinetic Books, Robert Malina)

Radioactive Decay. 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. \(\log _{6} 7-\log _{6} 9\)

Which pair of expressions in each list are equivalent? a. \(\log _{2} 11^{4}\) b. \(4 \log _{2} 11\) c. \(\left(\log _{2} 11\right)^{4}\)

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

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

Which pair of expressions in each list are equivalent? a. \(\ln \sqrt{t}\) b. \(\sqrt{\ln t}\) c. \(\frac{1}{2} \ln t\)

A feature article in a newspaper stated that the sport of snowboarding was growing exponentially. Explain what the author of the article meant by that.