91Ó°ÊÓ

Graph by hand or using a graphing calculator and state the domain and the range of each function. $$ g(x)=-2 \ln x $$

For each function, (a) determine whether it is one-to-one and (b) if it is one-to-one, find a formula for the inverse. $$f(x)=\frac{1}{x}$$

Atmospheric pressure \(P\) at altitude \(a\) is given by $$ P(a)=P_{0} e^{-0.00005 a} $$ where \(P_{0}\) is the pressure at sea level \(\approx 14.7 \mathrm{lb} / \mathrm{in}^{2}\) (pounds per square inch). Explain how a barometer, or some other device for measuring atmospheric pressure, can be used to find the height of a skyscraper.

Given \(\log _{b} 3=0.792 \text { and } \log _{b} 5=1.161\). If possible, use the properties of logarithms to calculate numerical values for each of the following. $$\log _{b} \sqrt{b^{3}}$$

Without using a calculator, explain why \(2^{\pi}\) must be greater than 8 but less than 16.

Solve. Where appropriate, include approximations to three decimal places. $$ \ln (x+5)+\ln (x+1)=\ln 12 $$

Suppose that \(\$ 1000\) is invested for 5 years at \(7 \%\) interest, compounded annually. In what year will the most interest be earned? Why?

Graph by hand or using a graphing calculator and state the domain and the range of each function. $$ g(x)=-\ln x $$

Given \(\log _{b} 3=0.792 \text { and } \log _{b} 5=1.161\). If possible, use the properties of logarithms to calculate numerical values for each of the following. $$\log _{b}(3 b)$$

Solve. Where appropriate, include approximations to three decimal places. $$ \ln (x-6)+\ln (x+3)=\ln 22 $$