Exam 5: Logarithmic Functions

Rewriting the statement $\log s=r$ using exponents gives

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 regression line for this data. Use the regression line to find the $y$ -value when $x=54$ . Give your answer correct to 2 decimal places.

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 regression line for this data. Use the regression line to find the value of $y$ when $x=18$ . Round to 2 decimal places.

What is the doubling time of a population growing by $12 \%$ per year? Round your answer to the nearest hundredth of a year.

Evaluate $10^{\log 13}$

The table below gives the number of ants living in a museum display. 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 regression line for this data. Use the regression line to calculate the number of ants after 24 months. Give your answer to the nearest whole number.

Solve $12 e^{2 t}-48=0$ for $t$ . Give your answer to 4 decimal places.