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.

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

The function given, \( a(t) = 5,000(1.12)^t \), represents exponential growth. In such a model, as time \( t \) increases, the amount \( a(t) \) grows slowly at first, but as \( t \) continues to increase, the growth rate accelerates, and the amount begins to increase more quickly.

Therefore, the correct answer is:

**Option #1: As t increases, a increases slowly at first and then quickly.**