Exam 5: Inverse, Exponential, and Logarithmic Functions

Ventilation is an effective way to improve indoor air quality. In nonsmoking restaurants, air circulation requirements (in ) are given by the function , where x is the number of people in the dining area. Find . Use to determine the maximum number of people that should be in a restaurant having a ventilation capability of 2,550 .

Solve the equation:

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 7-year loans at an interest rate of 7%. If a customer can afford to pay $108 per month, find the price of the most expensive car that can be purchased.

Solve the equation:

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 2010 if this trend continues.

Write the expression as one logarithm.

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

Write the expression as one logarithm. 9ln ( x ) - 8ln - 3ln ( xy )

How much money, invested at an interest rate of 12% per year compounded continuously, will amount to $91,000 after 16 years?

Write the expression as one logarithm.

The Gompertz function, is sometimes used to describe the sales of a new product whose sales are initially large but then level off toward a maximum saturation level. Graph the line and the Gompertz function with:

If $900 is deposited in a savings account that pays interest at a rate of % per year compounded continuously, find the balance after 7 years.

The graph of a one-to-one function f is shown. Find the domain D and range R of the inverse function .

The graph of a one-to-one function f is shown. Find the domain D and range R of the inverse function .

The radioactive bismuth isotope ²¹⁰ Bi has a half-life of 5 days. If there is 100 milligrams of ²¹⁰ Bi present at t = 0, then the amount f(t) remaining after t days is given by: How much ²¹⁰ Bi remains after 25 days?

Write the expression as one logarithm. 8ln ( x ) - 6ln - 3ln ( xy )

Sketch the graph of

Find the inverse function of .

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?

One method of estimating the thickness of the ozone layer is to use the formula , where I _o is the intensity of a particular wavelength of light from the sun before it reaches the atmosphere, I is the intensity of the same wavelength after passing through a layer of ozone x centimeters thick, and k is the absorption constant of ozone for that wavelength. Suppose a wavelength of cm with k = 0.45 , is measured as 1.14. Approximate the thickness of the ozone layer to the nearest 0.01 centimeter.