Exam 5: Exponential and Logarithmic Functions

The length (in centimeters) of a typical Pacific halibut t years old is approximately . What is the length of a typical 6-year-old Pacific halibut? How fast is the length of a typical 6-year-old Pacific halibut increasing? What is the maximum length a typical Pacific halibut can attain? Round your answers to the nearest tenth.

Simplify the expression.

Find the derivative of the function.

On the Richter scale, the magnitude R of an earthquake is given by the formula where I is the intensity of the earthquake being measured and is the standard reference intensity. What is the magnitude of an earthquake that has intensity 10 millions times that of ? __________ Suppose an earthquake is measured with a magnitude of 5 on the Richter scale with an error of at most 2%. Use differentials to find the error in the intensity of the earthquake. Hint: Observe that and use logarithmic differentiation. Round your answer to the nearest integer. __________

The strain (percent of compression) on the lumbar vertebral disks in an adult human as a function of the load x (in kilograms) is given by . What is the rate of change of the strain with respect to the load when the load is 300 kg? When the load is 450 kg? Give the answers to four decimal places.

Express the equation in logarithmic form.

Find the derivative of the function.

Find the derivative of the function.

Evaluate the expression.

Find an equation of the tangent line to the graph of at the point .

Find the present value of $50,000 due in 3 year(s) at the given rate of interest. 5% / year compounded monthly __________ 9% / year compounded daily __________

Simplify the expression.

The U.S. population is approximated by the function where P(t) is measured in millions of people and t is measured in 30-year intervals, with t = 0 corresponding to 1930. What is the expected population of the United States in 2050 ( t = 4 )?

If the temperature is constant, then the atmospheric pressure P (in pounds/square inch) varies with the altitude above sea level h in accordance with the law , where is the atmospheric pressure at sea level and k is a constant. If the atmospheric pressure is 15 at sea level and 13.5 at 5,000 ft, find the atmospheric pressure at an altitude of 15,000 ft. Please round the answer to one decimal place. __________ How fast is the atmospheric pressure changing with respect to altitude at an altitude of 15,000 ft? Please round the answer to four decimal places. __________

The length (in centimeters) of a common commercial fish is approximated by the von-Bertalanffy growth function where a, b, and k are positive constants. Select the graph of f.

Julio purchased 1,400 shares of a certain stock for $22,750 (including commissions). He sold the shares 6 year(s) later and received $32,100 after deducting commissions. Find the effective annual rate of return on his investment over the 6-year period.

Having received a large inheritance, a child's parents wish to establish a trust for the child's college education. If 7 year(s) from now they need an estimated $90,000, how much should they set aside in trust now, if they invest the money at the given rate of interest. Round your answer to the nearest cent. 15.5 compounded quarterly $__________ 15.5 compounded continuously $__________

Find the effective rate corresponding to the given nominal rate. Round your answers to two decimal places. 15% / year compounded semiannually _____% 9% / year compounded quarterly _____%

A certain piece of machinery was purchased 4 years ago by Garland Mills for $300,000. Its present resale value is $192,000. Assuming that the machine's resale value decreases exponentially, what will it be 3 years from now? Round your answer to the nearest dollar. $__________

Find the derivative of the function.