MAT 171 Sections 3.1-3.3

Use the compound interest formulas A = $$P(1+r/n)^{nt}$$ and $$A=Pe^{rt}$$ to solve. Find the accumulated value of an investment of $18,000 at 8% compounded annually for 14 years.

Write the equation in its equivalent exponential form. $$\log_3 x = 2$$

Write the equation in its equivalent logarithmic form. $$\sqrt[3]{8}=2$$

Find the domain of the logarithmic function. $$f(x) = \ln (4 - x)$$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$\log_5 (125x)$$

Expand: $$\log_{12}\left(\frac{12}{x}\right)$$

$$\log_2\left(\frac{x^4}{y^6}\right)$$

Use properties of logarithms to condense the logarithmic expression. Write the expression as logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. $$5\log_bt-\log_bs$$

A train ticket in a certain city is $2.00. People who use the train also have the option of purchasing a frequent rider pass for 18.75 each month. With the pass, each ticket costs only $1.25. Determine the number of times in a month the train must be used so that the total monthly cost without the pass is the same as the monthly cost with the pass.

You inherit $10,000 with the stipulation that for the first year the money must be invested in two stocks paying 6% and 11% annual interest, respectively. How much should be invested at each rate if the total interest earned for the year is to be $700?