Exam 5: Exponential and Logarithmic Functions

Julio purchased 1,400 shares of a certain stock for $22,750 (including commissions).He sold the shares 6 year(s) later and received $32,100 after deducting commissions.Find the effective annual rate of return on his investment over the 6-year period.

During a flu epidemic, the number of children in the Woodbridge Community School System who contracted influenza after t days was given by . How many children were stricken by the flu after the first day? How many children had the flu after 10 days? How many children eventually contracted the disease?

How long will it take $4,000 to grow to $7,500 if the investment earns interest at the rate of 15% / year compounded monthly? Round your answer to the nearest tenth. __________ year(s)

Use the laws of logarithms to simplify the expression.

The Ehrenberg equation gives the relationship between the height (in meters) and the average weight W (in kilograms) for children between 5 and 13 years of age. What is the average weight of a 10-year-old child who stands at 1.44 m tall? Round the answer to the nearest tenth.Use differentials to estimate the change in the average weight of a 10-year-old child whose height increases from 1.44 m to 1.49 m.

Find the inflection points of the function .

Eleni, who is now 55 years old, is employed by a firm that guarantees her a pension of $40,000/year at age 65.What is the present value of her first year's pension if inflation over the next 10 year(s) is at the given rate.Assume that inflation is continuously compounded. 4% _________ 8% _________ 19% _________

Use the definition of a logarithm to prove .Hint: Let and .Then, and .

Write the expression as the logarithm of a single quantity.

How long will it take an investment of $9,000 to double if the investment earns interest at the rate of 9% / year compounded monthly?

Find the effective rate corresponding to the given nominal rate.Round your answers to the nearest hundredth. 14% / year compounded semiannually __________% 5% / year compounded quarterly __________%

Having received a large inheritance, a child's parents wish to establish a trust for the child's college education.If 5 year(s) from now they need an estimated $60,000, how much should they set aside in trust now, if they invest the money at the given rate of interest. 17.5% compounded quarterly _________ 17)5% compounded continuously _________

Find the interest rate needed for an investment of $3,000 to grow to an amount of $7,500 in 3 year(s) if interest is compounded monthly.Round your answer to two decimal places.

Find the 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. $__________

Find the second derivative of the function.

Use the laws of logarithms to simplify the expression.

Express the equation in logarithmic form.

Find the derivative of the function.

A condominium complex was purchased by a group of private investors for $1.8 million and sold 6 year(s) later for $3.5 million.Find the annual rate of return (compounded continuously) on their investment.Round your answer to the nearest hundredth. __________%