Question

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

f(x) = 401.19(1.08)^x

Reason: an exponential model is f(x)=a·b^x. Using the endpoints, b ≈ (589/400)^(1/5) ≈ 1.08 and a ≈ 401.19 (rounded to the nearest hundredth), which matches the fourth option.