Question

Use the image to answer the question.

An increasing curve with an arrow on the upper end is plotted on a coordinate plane. The x-axis is labeled time left parenthesis years right parenthesis. The y-axis is labeled amount left parenthesis dollars right parenthesis.
▶Click for Long Desc

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)t
, where a is the amount after t years. Which one of the following statements is true about 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

Because a(t)=5000(1.12)^t is an exponential growth (base 1.12 > 1), the amount increases and the rate of increase gets larger over time — slowly at first, then more quickly.