Exam 5: Exponential and Logarithmic Functions

The monthly demand for a certain brand of table wine is given by the demand equation where p denotes the wholesale price per case (in dollars) and x denotes the number of cases demanded. Find the rate of change of the price to the nearest hundredth of a cent per case when x = 1,000. __________ cents per case What is the price per case when x = 1,000. $__________ / case

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.

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. __________%

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?

Use the laws of logarithms to simplify the expression.

The radioactive element polonium decays according to the law , where is the initial amount and the time t is measured in days.If the amount of polonium left after 420 days is 80 mg, what was the initial amount present? __________ mg

Find the derivative of the function.

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

Find the derivative of the function.

Find the inflection points of the function .

Find the derivative of the function.

Determine whether the statement is true or false.If it is true, explain why it is true.If it is false, give an example to show why it is false. The function is continuous on .

Evaluate the expression.

Simplify the expression.

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. $__________

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 concentration to four decimal places of the drug in the organ after 15 sec?

Evaluate the expression. = __________

Find the second derivative of the function.

The change from religious to lay teachers at Roman Catholic schools has been partly attributed to the decline in the number of women and men entering religious orders.The percent of teachers who are lay teachers is given by where t measured in decades, with corresponding to the beginning of 1960. What percent of teachers were lay teachers at the beginning of 1990? Please round the answer to one decimal place. __________ % How fast was the percent of lay teachers changing at the beginning of 1990? Please round the answer to two decimal places. __________ % / year Find the year when the percent of lay teachers was increasing most rapidly.

Find the derivative of the function.