Exam 5: Logarithmic Functions

What is the domain of $\sqrt{\left(e^{3 t}-7\right)^{2}-4}$ ?

If $11 \%$ of a radioactive substance decays in 6 hours, what percent of the substance is left after 11 hours? Round your answer to 3 decimal places, if necessary.

Use linear regression on the values $t$ and $\ln r$ to fit a function of the form $\ln r=b+m t$ . Use a calculator program to find the slope of the regression line for this data. Round to 4 decimal places.

What is the half-life of a substance that decays at a rate of $3.21 \%$ per day? Round your answer to the nearest hundredth of a day.

Use linear regression on the values $\mathrm{x}$ and $\ln y$ to fit a function of the form $\ln y=b+m x$ . Use a calculator program to find the vertical intercept of the regression line for this data. Round to 4 decimal places.

A small country is experiencing hyperinflation of $59 \%$ per month. A) By what percent have prices climbed after 5 months? B) If an item currently costs $\$ 12$ , how much will it cost after 1 year of such inflation?

You invest $\$ 4,000$ in an account earning $4 \%$ annual interest. At the same time, you invest $\$ 8,000$ in a different account earning $2 \%$ annual interest. In both accounts, the interest is compounded continuously. When do the accounts each hold the same amount? Round your answer to the nearest year.

What is the domain of the function $y=1+\ln (4-x)$ ?

Let $y=60 e^{-0.07 t}$ , with $t$ measured in years. What is the percent annual decay rate? Round to 2 decimal places.

Find $\lim _{x \rightarrow 5^{+}} \ln (5-x)$ .

What is the range of the function $y=\ln \left(\frac{x}{3}\right)$ ?

Solve $\log x=2$ for $x$ .

Solve $4^{x}=9$ using logs. Give your answer to 3 decimal places.

Evaluate $\ln \left(e^{9}\right)$

If you wished to graph the number of cancer cases in the US per year over the past 50 years on a standard sheet of paper, would you use a standard or a logarithmic scale?

What is the hydrogen ion concentration $\left[\mathrm{H}^{+}\right]$ for a substance with a $\mathrm{pH}$ of 6.3 ? Express your answer as a power of 10 .

If $11 \%$ of a radioactive substance decays in 8 hours, what is the half-life of the substance in hours? Round your answer to 3 decimal places.

Let $m=\log q$ . What is $\log (100,000 q)$ ?

Suppose earthquake A measured 3.6 on the Richter scale. What was the Richter scale measure of earthquake B if it was 1700 times more powerful than earthquake A? Round your answer to 2 decimal places.

The following table gives $v$ as a linear function of $w$ . If $w=\ln x$ and $v=\ln y$ , find a formula for $y$ in terms of $x$ .