Exam 20: Exponential and Logarithmic Functions

A father invests $\$ 7500$ in a savings account that earns $5.4 \%$ interest compounded annually when his child is born. What will the value of the account be after 18 years when the child is ready to go to college or university?

A particular radioactive isotope decreases exponentially at a rate of $24 \%$ per year. How long will it take for the amount of the isotope to quarter?

Graph $y=0.4 x^{0.75}$ on log-log paper.

Solve for $x$ : $\log _{x} 64=3 / 2$

Solve for $x$ to three significant digits. Check your answers. [HINT: $\log x=\log _{10} x$ ] $\log (10 x-2)+\log 2=\log (2 x+10)-\log 2$

The atmospheric pressure $p$ decreases exponentially with the height $h$ (in kilometres) above the Earth according the function $p=101.1 e^{-h / 6.4}(\mathrm{KPa})$ . Determine the height at which the atmospheric pressure is $25 \mathrm{kPa}$ .

Solve for $x:(2-\log x)(1-2 \log x)+1=0$

Find the common logarithm of each number to four decimal places: (a) 28.1 (b) 9.51 (c) 10.003 (d) 0.0081

Write as the sum or difference of two or more logarithms: $\log \frac{9}{8}$

Convert to logarithmic form: $e^{2 x}=y$

Solve for $x$ to three significant digits. Check your answers. [HINT: $\left.\log x=\log _{10} x\right]$ $\log (x+1)+\log x=\log 6$

Write as the sum or difference of two or more logarithms: $\log \frac{x^{4}}{y \sqrt[3]{z}}$

A certain isotope of silver, ${ }^{110} \mathrm{Ag}$ decays at a rate of $2.8 \%$ per second. After 50.0 seconds, what percent of the original isotope remains?

Find the amount to which $\$ 250$ will accumulate in 7 years at a compound interest rate of $3 \%$ per year, compounded annually.

Solve for $x$ to three significant digits: $3^{X}=8$

Rewrite the equation so that it contains no logarithms: $2 \log x-3 \log y=1$

Convert to logarithmic form: $3^{5}=243$

Graph the following function from $x=1 / 4$ to $x=4$ : $y=-0.3 \log _{4} 2 x$

Convert to exponential form: $\log _{X} 5=z$

Solve for $x: \log \left(x^{2}-9\right)-3=\log (x+3)$