91Ó°ÊÓ

The formula \(A=P(1+r)^{t}\) expresses the amount \(A\) to which \(P\) dollars will increase if invested for \(t\) years at a rate of \(r\) per year. Find \(A\) when \(P=\$ 500, r=0.04\) and \(t=5\)

In \(23-34,\) evaluate each function for the given value. Be sure to show your work. $$ \mathrm{f}(x)=\left(\frac{x^{-1}}{(2 x)^{-2}}\right)^{-1} ; \mathrm{f}(8) $$

The formula \(A=P(1+r)^{t}\) expresses the amount \(A\) to which \(P\) dollars will increase if invested for \(t\) years at a rate of \(r\) per year. Find the amount to which \(\$ 2,400\) will increase when invested at 5\(\%\) for 10 years.

Solve each equation and check. \((0.01)^{2 x}=100^{2-x}\)

In \(3-37,\) express each power as a rational number in simplest form. $$ 125^{\frac{2}{3}} \div 125^{\frac{1}{3}} $$

In \(23-34,\) evaluate each function for the given value. Be sure to show your work. $$ f(x)=\frac{1}{1+\frac{2}{x^{-1}}} ; f(-5) $$

In \(3-37,\) express each power as a rational number in simplest form. $$ 4^{0}+4^{-\frac{1}{2}} $$

The formula \(A=P(1+r)^{t}\) expresses the amount \(A\) to which \(P\) dollars will increase if invested for \(t\) years at a rate of \(r\) per year. What is the minimum number of years that \(\$ 1\) must be in invested at 5\(\%\) to increase to \(\$ 2 ?\) (Use a calculator to try possible values of \(t.\))

Solve each equation and check. \((0.25)^{x-2}=4^{x}\)

In \(23-34,\) evaluate each function for the given value. Be sure to show your work. $$ \mathrm{f}(x)=4\left(\frac{1}{2}\right)^{-x}+3\left(\frac{1}{2}\right)^{-x} ; \mathrm{f}(3) $$