Question

Lincoln's parents invested $5,000 in a college savings account when he was born. If the account has a growth rate of 12%, the situation can be
modeled by the equation a (t) = 5,000(1.12)*
, where a is the amount after t years. Which one of the following statements is true aout the
graph of the function?
Option #1: As t increases, a increases slowly at first and then quickly.
Option $2: As t increases, a increases quickly at first and then slowly.
Option #3: As t increases, a decreases slowly at first and then quickly.
Option #4: As t increases, a decreases quickly at first and then slowly.
(1 point)
Option #
is the true statement

Answer 1

Option #1.

Since a(t) = 5000(1.12)^t with base 1.12 > 1, the function is increasing and its rate of increase grows (a''(t) > 0). So it rises slowly at first and then more quickly (compounding growth).