Question

Using the Regression Calculator to Find an Exponential Model
Miguel invested $400 in a bank account that pays interest. The account’s value over time, in x years, is given in the table.

A 2-column table with 6 rows. The first column is labeled time (years) with entries 0, 1, 2, 3, 4, 5. The second column is labeled account value (dollar sign) with entries 400, 436, 468, 502, 550, 589.
Which exponential function models the data? Round the numerical values to the nearest hundredth.

f(x) = 1.41(30.69)x
f(x) = 37.74(396.48)x
f(x) = 390.60(1.41)x
f(x) = 401.19(1.08)x

Answer 1

Use exponential regression (fit y = a·b^x) to the given data. The best-fit parameters are a ≈ 401.19 and b ≈ 1.08.

So the model is f(x) = 401.19(1.08)^x (rounded to the nearest hundredth).