91Ó°ÊÓ

If the purchasing power of \(\$ 1000\) is only \(\$ 930\) after 2 years, what was the average inflation rate?

Write each expression as a single logarithm. \(\log _{2}\left(\frac{1}{x}\right)+\log _{2}\left(\frac{1}{x^{2}}\right)\)

Solve each exponential equation. Express irrational solutions in exact form. $$ e^{x+3}=\pi^{x} $$

The function \(f\) is one-to-one. (a) Find its inverse function \(f^{-1}\) and check your answer. (b) Find the domain and the range of \(f\) and \(f^{-1}\). $$ f(x)=\frac{3 x+4}{2 x-3} $$

Automobile Production The number \(N\) of cars produced at a certain factory in one day after \(t\) hours of operation is given by \(N(t)=100 t-5 t^{2}, 0 \leq t \leq 10 .\) If the cost \(C\) (in dollars) of producing \(N\) cars is \(C(N)=15,000+8000 N\), find the cost \(C\) as a function of the time \(t\) of operation of the factory.

Graph each function and its inverse on the same set of axes. $$ f(x)=3^{x} ; f^{-1}(x)=\log _{3} x $$

Write each expression as a single logarithm. \(\log _{4}\left(x^{2}-1\right)-5 \log _{4}(x+1)\)

Solve each exponential equation. Express irrational solutions in exact form. $$ 2^{2 x}+2^{x}-12=0 $$

Solve each exponential equation. Express irrational solutions in exact form. $$ 3^{2 x}+3^{x}-2=0 $$

Environmental Concerns The spread of oil leaking from a tanker is in the shape of a circle. If the radius \(r\) (in feet) of the spread after \(t\) hours is \(r(t)=200 \sqrt{t},\) find the area \(A\) of the oil slick as a function of the time \(t .\)