91Ó°ÊÓ

For each function, (a) determine whether it is one-to-one and (b) if it is one-to-one, find a formula for the inverse. $$f(x)=x+2$$

Use a calculator to find each of the following rounded to four decimal places. $$ 10^{4.8982} $$

The bacteria Escherichia coli (E. coli) are commonly found in the human bladder. Suppose that 3000 of the bacteria are present at time \(t=0 .\) Then \(t\) minutes later, the number of bacteria present is $$ N(t)=3000(2)^{t / 20} $$ If \(100,000,000\) bacteria accumulate, a bladder infection can occur. If, at 11: 00 A.M., a patient's bladder contains \(25,000 E\) coli bacteria, at what time can infection occur?

Review factoring polynomials (Sections \(6.1-6.6)\) Factor $$ 5 x^{4}-10 x^{3}-3 x^{2}+6 x $$

Solve. Where appropriate, include approximations to three decimal places. $$ \log _{4}(x+6)-\log _{4} x=2 $$

Use the properties of logarithms to find each of the following. $$\log _{3}(9 \cdot 81)$$

Rewrite each of the following as an equivalent exponential equation. Do not solve. $$ \log _{10} 0.01=-2 $$

Rewrite each of the following as an equivalent exponential equation. Do not solve. $$ \log _{e} 0.989=-0.0111 $$

Solve for \(x\) $$ \log \left(275 x^{2}\right)=38 $$

Rewrite each of the following as an equivalent logarithmic equation. Do not solve. $$ e^{3}=20.0855 $$