Home Prices The median price of a home in the United States declined conti...

Home Prices The median price of a home in the United States declined continuously over the period 2005–2008 at a rate of 5.5% per year from around $230 thousand in 2005. Write down a formula that predicts the median price of a home t years after 2005. Use your model to estimate the median home price in 2007 and 2010. HINT [See Example 5.]

Example 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: