Exam 5: Exponential and Logarithmic Functions

Skeletal remains of the so-called "Pittsburgh Man", unearthed in Pennsylvania, had lost 86% of the carbon 14 they originally contained. Determine the approximate age of the bones. Hint: the decay constant k for carbon 14 is equal to 0.00012.

The concentration of a drug in an organ at any time t (in seconds) is given by where x(t) is measured in grams/cubic centimeter . Sketch the graph of x.

Solve the equation for x.

Find the present value of $58,669 due in 5 year(s) at an interest rate of 7% / year compounded continuously. Round your answer to the nearest dollar. $__________

According to estimates by Paul Kroger Associates, the percent of households that own VCRs is given by where t is measured in years, with t = 0 corresponding to the beginning of 1985. What percent of households owned VCRs at the beginning of 1985? At the beginning of 1994?

Find the derivative of the function.

Find the derivative of the function.

Find the derivative of the function.

According to estimates by Paul Kroger Associates, the percent of households that own VCRs is given by , where t is measured in years, with t = 0 corresponding to the beginning of 1985. What percent of households owned VCRs at the beginning of 1985? Round your answer to the nearest tenth. __________% At the beginning of 1993?. Round your answer to the nearest tenth. __________%

On the basis of data collected during an experiment, a biologist found that the growth of the fruit fly (Drosophila) with a limited food supply could be approximated by the exponential model where t denotes the number of days since the beginning of the experiment. How fast was the population changing on the 20th day?

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

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

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

How long will it take an investment of $7,000 to double if the investment earns interest at the rate of 7% compounded continuously? Round your answer to two decimal places.

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. Suppose an earthquake is measured with a magnitude of 6 on the Richter scale with an error of at most 2%. Use differentials to find the error in the intensity of the earthquake. Round your answer to the nearest integer.

The concentration of a drug in grams/cubic centimeter (g/cm3) t minutes after it has been injected into the bloodstream is given by where u, l, and k are positive constants, with l > u. At what time is the concentration of the drug the greatest? What will be the concentration of the drug in the long run?

Simplify the expression.

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

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