91Ó°ÊÓ

Find a linear function whose graph has the given characteristics. Perpendicular to \(y=\frac{1}{2} x+3 ; y\) -intercept: \((0,8)\)

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

Factor. $$ 3 x^{2}-48 $$

Solve. Where appropriate, include approximations to three decimal places. If no solution exists, state this. $$ \log (2 x+1)=1 $$

Express as an equivalent expression that is a single logarithm and, if possible, simplify. $$2 \log _{b} w-\log _{b} z-4 \log _{b} y$$

Rewrite each of the following as an equivalent exponential equation. Do not solve. $$ \log _{9} 9=1 $$

For each function, (a) determine whether it is one-to-one; (b) if it is one- to-one, find a formula for the inverse. \(f(x)=\frac{3 x+2}{5}\)

Express as an equivalent expression that is a single logarithm and, if possible, simplify. $$3 \log _{c} p+\frac{1}{2} \log _{c} t-\log _{c} 7$$

Atmospheric pressure \(P\) at an elevation \(a\) feet above sea level can be estimated by $$ P=P_{0} e^{-0.00004 a} $$ where \(P_{0}\) is the pressure at sea level, which is approximately 29.9 in. of mercury (Hg). Explain how a barometer, or some other device for measuring atmospheric pressure, can be used to find the height of a skyscraper.

Rewrite each of the following as an equivalent exponential equation. Do not solve. $$ \log _{6} 36=2 $$