Exam 5: Inverse, Exponential, and Logarithmic Functions

An urban density model is a formula that relates the population density D ( in thousands/ mi ² ) to the distance x (in miles) from the center of the city. The formula for the central density a and coefficient of decay b has been found to be appropriate for many large U.S. cities. For the city of Atlanta in 1970, a = 5.5 and b = 0.10. At approximately what distance was the population density 1,800 per square mile?

Use common logarithms to solve for x in terms of y.

Sketch the graph of the function.

Determine the range of for the function without actually finding . Hint: First find the domain and range of

Sketch the graph of

In 1980, the population of blue whales in the southern hemisphere was thought to number 5,000. The population N(t) has been decreasing according to the formula where t is in years and t = 0 corresponds to 1980. Predict the population in the year 2020 if this trend continues.

If $1,200 is deposited in a savings account that pays interest at a rate of % per year compounded continuously, find the balance after 4 years.

The graph of a one-to-one function f is shown. Use the reflection property to sketch the graph of

Solve the equation without using a calculator.

Solve the equation.

Use the theorem on inverse functions to determine whether f and g are inverse functions of each other.

Solve the equation.

Change to exponential form.

Express in terms of logarithms of x, y, or z.

An economist suspects that the points lie on the graph of , where and are constants. If the data points have three-decimal-place accuracy, is this suspicion correct?

When the volume control on a stereo system is increased, the voltage across a loudspeaker changes from V ₁ to V ₂ , and the decibel increase is given by Find the decibel increase if the voltage changes from 1.7 volts to 3 volts.

Write the expression as one logarithm.

Graph f on the given interval. Estimate the largest interval [ a , b ] with a < 0 < b on which f is one-to-one.

Some lending institutions calculate the monthly payment M on a loan of L dollars at an interest rate r (expressed as a decimal) by using the formula: where k = [1 + ( r / 12 )] ^12t and t is the number of years that the loan is in effect. An automobile dealer offers customers no-down-payment 8-year loans at an interest rate of 10%. If a customer can afford to pay $122 per month, find the price of the most expensive car that can be purchased.

Use the theorem on inverse functions to determine whether f and g are inverse functions of each other.