91Ó°ÊÓ

Rewrite each of the following as an equivalent expression with rational exponents. $$ \sqrt[4]{x^{12}}, \quad x \geq 0 $$

Graph. $$ f(x)=\left\\{\begin{array}{ll} -7, & \text { for } x=2 \\ x^{2}-3, & \text { for } x \neq 2 \end{array}\right. $$

Graph. $$ f(x)=\left\\{\begin{array}{ll} -6, & \text { for } x=-3 \\ -x^{2}+5, & \text { for } x \neq-3 \end{array}\right. $$

Hanna's Photography spends \(\$ 40\) per square foot on improvements to a \(25,000-\mathrm{ft}^{2}\) office space. Under IRS guidelines for straight-line depreciation, these improvements will depreciate completely-that is, have zero salvage value-after \(39 \mathrm{yr}\). Find the depreciated value of the improvements after \(10 \mathrm{yr}\).

Rewrite each of the following as an equivalent expression with rational exponents. $$ \sqrt[3]{t^{6}} $$

The Video Game Wizard buys a new computer system for \(\$ 60,000\) and projects that its book value will be \(\$ 2000\) after 5 yr. Using straight-line depreciation, find the book value after 3 yr.

Rewrite each of the following as an equivalent expression with rational exponents. $$ \frac{1}{\sqrt{t^{5}}} $$

The amount of money, \(A(t),\) in \(a\) savings account that pays 3\% interest, compounded quarterly for \(t\) years, with an initial investment of \(P\) dollars, is given by $$ A(t)=P\left(1+\frac{0.03}{4}\right)^{4 t} $$ If \(\$ 500\) is invested at \(3 \%\), compounded quarterly, how much will the investment be worth after 2 yr?

Rewrite each of the following as an equivalent expression with rational exponents. $$ \frac{1}{\sqrt{m^{4}}} $$

Tyline Electric uses the function \(B(t)=-700 t+3500\) to find the book value, \(B(t)\) in dollars, of a photocopier \(t\) years after its purchase. a) What do the numbers -700 and 3500 signify? b) How long will it take the copier to depreciate completely? c) What is the domain of \(B\) ? Explain.