Review Exercises

$f\left(x\right)=7x-2$ and
$g\left(x\right)=5x+1$

For functions
$f\left(x\right)=3x^2+2$ and
$g\left(x\right)=4x-3,$ find
ⓐ $\left(f\circ g\right)\left(\mathrm{-3}\right)$
ⓑ $\left(g\circ f\right)\left(\mathrm{-2}\right)$
ⓒ $\left(f\circ f\right)\left(\mathrm{-1}\right)$

$\{\left(\mathrm{-3},\mathrm{-5}\right),\left(\mathrm{-2},\mathrm{-4}\right),\left(\mathrm{-1},\mathrm{-3}\right),\left(0,\mathrm{-2}\right),$
$\left(\mathrm{-1},\mathrm{-1}\right),\left(\mathrm{-2},0\right),\left(\mathrm{-3},1\right)\}$

$\{\left(\mathrm{-3},3\right),\left(\mathrm{-2},1\right),\left(\mathrm{-1},\mathrm{-1}\right),\left(0,\mathrm{-3}\right),$
$\left(1,\mathrm{-5}\right),\left(2,\mathrm{-4}\right),\left(3,\mathrm{-2}\right)\}$

ⓐ

ⓑ

$f\left(x\right)=2x+9$ and
$g\left(x\right)=\frac{x+9}{2}$

$f\left(x\right)=x^3+13$

$f\left(x\right)=\sqrt[5]{x-1}$

$f\left(x\right)={\left(\frac{1}{5}\right)}^x$

$g\left(x\right)=3^{x+2}$

$f\left(x\right)=e^x+5$

$3^{5x-6}=81$

$9^x=27$

$e^{4x}·e^7=e^{19}$

Felix invested $\text{\$}\mathrm{12,000}$ in a savings account. If the interest rate is $4\text{\%}$ how much will be in the account in 12 years by each method of compounding?

ⓐ compound quarterly
ⓑ compound monthly
ⓒ compound continuously.

A researcher at the Center for Disease Control and Prevention is studying the growth of a bacteria. She starts her experiment with 150 of the bacteria that grows at a rate of $15\text{\%}$ per hour. She will check on the bacteria every 24 hours. How many bacteria will he find in 24 hours?

$5^4=625$

${63}^{\frac{1}{5}}=\sqrt[5]{63}$

$7={\text{log}}_{2}128$

$4=\text{ln}x$

${\text{log}}_{7}x=\mathrm{-2}$

${\text{log}}_{2}32$

${\text{log}}_3\frac{1}{9}$

$y={\text{log}}_{\frac{1}{4}}x$

${\text{log}}_{a}36=5$

${\text{log}}_2\left(5x-7\right)=3$

$\text{log}(x^2-21)=2$

ⓐ ${\text{log}}_{7}1$ ⓑ ${\text{log}}_{12}12$

ⓐ ${10}^{\text{log}\sqrt{5}}$ ⓑ $\text{log}{10}^{\mathrm{-3}}$

${\text{log}}_4\left(64xy\right)$

${\text{log}}_7\frac{49}{y}$

$\text{log}{x}^{\mathrm{-9}}$

${\text{log}}_3\left(\sqrt{4}{x}^7{y}^8\right)$

$\text{ln}\frac{\sqrt{3x^2-y^2}}{z^4}$

${\text{log}}_{2}56-{\text{log}}_{2}7$

${\text{log}}_5\left(x^2-16\right)-2{\text{log}}_5\left(x+4\right)$

${\text{log}}_{5}97$

$3{\text{log}}_{5}x={\text{log}}_{5}216$

$\text{log}\left(x-1\right)-\text{log}\left(3x+5\right)=\text{−}\text{log}x$

$\text{ln}\left(3x-2\right)=\text{ln}\left(x+4\right)+\text{ln}2$

$e^x=23$

$7e^{x+3}=28$

Jerome invests $\text{\$}\mathrm{18,000}$ at age 17. He hopes the investments will be worth $\text{\$}\mathrm{30,000}$ when he turns 26. If the interest compounds continuously, approximately what rate of growth will he need to achieve his goal? Is that a reasonable expectation?

Researchers recorded that a certain bacteria population grew from 100 to 300 in 8 hours. At this rate of growth, how many bacteria will there be in 24 hours?

The half-life of radioactive iodine is 60 days. How much of a 50 mg sample will be left in 40 days?