Obtain exponential functions in the form in Exercise. HINT [See Example 5.] Exercis...

Obtain exponential functions in the form in Exercise. HINT [See Example 5.]

Exercise 5:

a. You invest $10,000 at Fastrack Savings & Loan, which pays 6% compounded continuously. Express the balance in your account as a function of the number of years t and calculate the amount of money you will have after 5 years.

b. Your friend has just invested $20,000 in Constant Growth Funds, whose stocks are continuously declining at a rate of 6% per year. How much will her investment be worth in 5 years?

c. During which year will the value of your investment first exceed that of your friend?

Solution

a. We use the continuous growth formula with P = 10,000, r = 0.06, and t variable, getting

In five years,

b. Because the investment is depreciating, we use a negative value for r and take P = 20,000, r = −0.06, and t = 5, getting

c. We can answer the question now using a graphing calculator, a spreadsheet, or the Function Evaluator and Grapher tool at the Web site. Just enter the exponential models of parts (a) and (b) and create tables to compute the values at the end of several years:

f (t) is the value after t years of a $10,000 investment depreciating continuously at an annual rate of 60%.