91Ó°ÊÓ

Salvage Value. A laser printer is purchased for \(\$ 1200 .\) Its value each year is about \(80 \%\) of the value of the preceding year. Its value, in dollars, after \(t\) years is given by the exponential function $$ V(t)=1200(0.8)^{t} $$ a) Find the value of the printer after 0 year, 1 year, 2 years, 5 years, and 10 years. b) Graph the function.

Solve. Where appropriate, include approximations to three decimal places. If no solution exists, state this. $$ 3 \ln x=-3 $$

Find each of the following logarithms using the change. of-base formula. Round answers to four decimal places. $$ \log _{\pi} 10 $$

As a result of preservation efforts in most countries in which whaling was common, the humpback whale population has grown since the 1970 s. The worldwide population of humpbacks, \(P(t),\) in thousands, \(t\) years after 1982 can be approximated by $$ P(t)=5.5(1.047)^{t} $$ a) How many humpback whales were alive in \(1992 ?\) in \(2004 ?\) b) Graph the function.

For each function, (a) determine whether it is one-to-one; (b) if it is one- to-one, find a formula for the inverse. \(h(x)=-10-x\)

Express as an equivalent expression, using the individual logarithms of \(w, x, y,\) and \(z\) $$\log _{a} \sqrt[3]{\frac{x^{6} y^{3}}{a^{2} z^{7}}}$$

Solve. Where appropriate, include approximations to three decimal places. If no solution exists, state this. $$ \log _{5}(7-2 x)=3 $$

Find each of the following logarithms using the change. of-base formula. Round answers to four decimal places. $$ \log _{\pi} 100 $$

Express as an equivalent expression, using the individual logarithms of \(w, x, y,\) and \(z\) $$\log _{a} \sqrt[4]{\frac{x^{8} y^{12}}{a^{3} z^{5}}}$$

For each function, (a) determine whether it is one-to-one; (b) if it is one- to-one, find a formula for the inverse. \(h(x)=7-x\)