Question

Determining the Regression Equation
Mr. Valdez puts $10,000 in a retirement account and does not make any deposits or withdrawals. The table below shows the amount of money in the account after x years.

A 2-column table with 5 rows. The first column is labeled years with entries 0, 10, 20, 30, 40. The second column is labeled amount (dollar sign) with entries 10,000; 16,000; 27,000; 43,000; 70,000.
What values, rounded to the nearest hundredth, complete the exponential regression equation that models the data?



f(x) =
(
)x

Answer 1

The exponential regression is of the form f(x) = a·b^x. Fitting ln y = ln a + x ln b to the data gives

a ≈ 9974.73 and b ≈ 1.05,

so f(x) ≈ 9974.73(1.05)^x (values rounded to the nearest hundredth).