Exam 5: Exponential and Logarithmic Functions

The monthly demand for a certain brand of perfume is given by the demand equation where p denotes the retail unit price (in dollars) and x denotes the quantity (in 1-oz bottles) demanded. Find the rate of change of the price to the nearest hundredth of a cent per bottle when x = 2,000. __________ cents per bottle What is the price per bottle when x = 2,000. $__________ / bottle

Solve the equation for x.

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

Find the derivative of the function.

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. $__________

Based on data obtained from the Census Bureau, the manager of Plymouth Van Lines estimates that the percent of the total population relocating in year t ( corresponds to the year 1960) may be approximated by the formula . Compute , , and .

Find the derivative of the function.

Suppose a radioactive substance decays according to the formula .How long will it take for the substance to decay to half the original amount?

The monthly demand for a certain brand of perfume is given by the demand equation where p denotes the retail unit price (in dollars) and x denotes the quantity (in 1-oz bottles) demanded.Find the rate of change of the price to the nearest hundredth of a cent per bottle when x = 1,000.

Evaluate the expression.

Find the accumulated amount A if the principal P is invested at an interest rate of r per year for t years.Round your answer to the nearest cent. P = $180,000, r = 6%, t = 5, compounded daily $__________

Use the laws of logarithms to simplify the expression.

Find the second derivative of the function.

Solve the equation for x.

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.

Simplify the expression.

Wood deposits recovered from an archeological site contain 25% of the carbon 14 they originally contained.How long ago did the tree from which the wood was obtained die? Hint: the decay constant k for carbon 14 is equal to 0.00012.

Find the nominal interest rate that, when compounded continuously, yields an effective interest rate of 10% / year.Round your answer to the nearest thousandth. __________%

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?

A condominium complex was purchased by a group of private investors for $1.3 million and sold 6 year(s) later for $3.4 million.Find the annual rate of return (compounded continuously) on their investment.