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. Round your answer to the nearest year. Hint: the decay constant k for carbon 14 is equal to 0.00012. __________ years

The height (in feet) of a certain kind of tree is approximated by where is the age of the tree in years. Estimate the age of an 70-ft tree. Round your answer to the nearest hundredth.

Write the expression as the logarithm of a single quantity.

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 . Select the graph of x.

Find the derivative of the function.

The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by . What is the price of the commodity at t = 0? $__________ / unit How fast is the price of the commodity decreasing at t = 0? $__________ / wk Find the equilibrium price of the commodity. (Hint: It's given by . Also, use the fact that .) $__________ / unit

Find the derivative of the function.

Express the equation in logarithmic form.

Determine the intervals where the function is increasing.

Evaluate the expression.

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

Find the second derivative of the function.

The Estradas are planning to buy a house 4 year(s) from now. Housing experts in their area have estimated that the cost of a home will increase at a rate of 7% / year during that 4-year period. If this economic prediction holds true, how much can they expect to pay for a house that currently costs $60,000? Round your answer to the nearest cent. $__________

Strontium 90, a radioactive isotope of strontium, is present in the fallout resulting from nuclear explosions. It is especially hazardous to animal life, including humans, because, upon ingestion of contaminated food, it is absorbed into the bone structure. Its half-life is 27 years. If the amount of strontium 90 in a certain area is found to be four times the "safe" level, find how much time must elapse before an "acceptable level" is reached. __________ years

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

Julio purchased 1,100 shares of a certain stock for $26,750 (including commissions). He sold the shares 5 year(s) later and received $32,500 after deducting commissions. Find the effective annual rate of return on his investment over the 5-year period. Round your answer to the nearest hundredth. __________%

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.

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

The height (in feet) of a certain kind of tree is approximated by where t is the age of the tree in years. Estimate the age of an 75-ft tree. Please round the answer to two decimal places.

Solve the equation for x.