Exam 5: Exponential and Logarithmic Functions

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 at sea level and at 5,000 ft, how fast is the atmospheric pressure changing with respect to altitude at an altitude of 15,000 ft? Give the answer to four decimal places.

Express the equation in logarithmic form.

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

The concentration of a drug in an organ at any time t (in seconds) is given by where C(t) is measured in milligrams/cubic centimeter . What is the initial concentration of the drug in the organ? __________ What is the concentration to four decimal places of the drug in the organ after 10 sec? __________ What is the concentration to four decimal places of the drug in the organ after 30 sec? __________ What will be the concentration of the drug in the long run? __________

Find the nominal interest rate that, when compounded monthly, yields an effective interest rate of 6% / year.

Evaluate the expression.

Find the derivative of the function.

Find the derivative of the function.

Find the derivative of the function.

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.How fast was the total federal debt increasing in 2002? round answer to three decimal places.

Use logarithms to solve the equation for t.

Solve the equation for x.

Find the derivative of the function.

Find the interest rate needed for an investment of $4,000 to grow to an amount of $8,500 in 2 year(s) if interest is compounded monthly.Round your answer to the nearest hundredth. __________%

Find the accumulated amount after 3 year(s) if $6,000 is invested at 8% compounded continuously.

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)? Round your answer to one decimal place. __________ million

Find the nominal interest rate that, when compounded continuously, yields an effective interest rate of 20% / year.

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

Find the second derivative of the function.