Exam 5: Exponential and Logarithmic Functions

Use the laws of logarithms to simplify the expression.

Three hundred students attended the dedication ceremony of a new building on a college campus. The president of the traditionally female college announced a new expansion program, which included plans to make the college coeducational. The number of students who learned of the new program t hours later is given by the function . If 600 students on campus had heard about the new program 2 hours after the ceremony, how many students had heard about the policy after 4 hours?

Phosphorus 32 has a half-life of 14.2 days. If 100 g of this substance are present initially, find the amount present after t days. What amount will be left after 7.1 days? How fast is the phosphorus 32 decaying when t = 7.1?

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?

A certain piece of machinery was purchased 4 year(s) ago by Garland Mills for $400,000. Its present resale value is $256,000. Assuming that the machine's resale value decreases exponentially, what will it be 2 year(s) from now?

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

How long will it take $4,000 to grow to $7,500 if the investment earns interest at the rate of 15% / year compounded monthly? Round your answer to the nearest tenth. __________ year(s)

For children between the ages of 5 and 13 years old, the Ehrenberg equation gives the relationship between the weight W (in kilograms) and the height h (in meters) of a child. Use differentials to estimate the change in the weight of a child who grows from 0.8 m to 1 m. Round the answer to the nearest tenth. __________ kg

Find the effective rate corresponding to the given nominal rate. Round your answers to the nearest hundredth. 14% / year compounded semiannually __________% 5% / year compounded quarterly __________%

The growth rate of the bacterium, a common bacterium found in the human intestine, is proportional to its size. Under ideal laboratory conditions, when this bacterium is grown in a nutrient broth medium, the number of cells in a culture doubles approximately every 20 min. If the initial cell population is 100, determine the function Q(t) that expresses the exponential growth of the number of cells of this bacterium as a function of time t (in minutes). How long will it take for a colony of 100 cells to increase to a population of 1 million? If the initial cell population were 1,000, how would this alter the model?

Find the derivative of the function.

Use the curve-sketching guideline, to select the graph of the function.

Sketch the graphs of the given functions on the same axes.

Use the laws of logarithms to simplify the expression.

Find the derivative of the function.

Use logarithmic differentiation to find the derivative of the function.

According to data obtained from the CBO, the total federal debt (in trillions of dollars) from 2001 through 2006 is given by where t is measured in years, with corresponding to 2001. What was the total federal debt in 2004? Round answer to three decimal places.

Find the derivative of the function.

Use logarithms to solve the equation for t. Round your answer to four decimal places. t = __________

Find the derivative of the function.