Exam 5: Inverse, Exponential, and Logarithmic Functions

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.

If $1,100 is deposited in a savings account that pays interest at a rate of % per year compounded continuously, find the balance after 4 years.

Sketch the graph of

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 4-year loans at an interest rate of 15%. If a customer can afford to pay $229 per month, find the price of the most expensive car that can be purchased.

Change to logarithmic form.

Solve the equation:

If 3 grams of salt is added to a quantity of water, then the amount that is undissolved after t minutes is given by: Sketch a graph that shows the value at any time from t = 0 to t = 10.

Find the inverse function of .

Use the change of base formula to approximate the x-intercept.

Simplify the expression.

Find the solution of the equation.

If 7 grams of salt is added to a quantity of water, then the amount that is undissolved after t minutes is given by: Sketch a graph that shows the value at any time from t = 0 to t = 10.

Solve the equation.

If $800 is deposited in a savings account that pays interest at a rate of % per year compounded continuously, find the balance after 7 years.

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 2,800 per square mile?

Change to exponential form.

Sketch the graph of the function.

Find an exponential function of the form f (x) = ba ^x that has the given y-intercept and passes through the point P: y-intercept = 64; P (3,1);

Solve the equation:

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