Question

The table shows the value of an account x years after the account was opened.

A 2-column table with 5 rows. The first column is labeled years after opening account with entries 0, 2, 5, 8, 10. The second column is labeled account value (in dollars) with entries 5,000; 5,510; 6,390; 7,390; 8,150.
Based on the exponential regression model, which is the best estimate of the value of the account 12 years after it was opened?

$8,910
$8,980
$13,660
$16,040

Answer 1

Exponential model A(t) = ab^t. Since A(0)=5000, a = 5000. Estimate b ≈ (A(10)/A(0))^(1/10) = (8150/5000)^(1/10) ≈ 1.05. Then

A(12) ≈ 5000*(1.05)^12 ≈ 5000*1.796 ≈ $8,980.

Answer: $8,980.