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

Question

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, \( a(t) = 5000(1.12)^t \), is an exponential growth function because the base (1.12) is greater than 1.

In an exponential growth function:

• The value of \( a(t) \) starts relatively small when \( t \) is small.
• As \( t \) increases, \( a(t) \) grows at an increasing rate, meaning it increases slowly at first and then more rapidly over time.

Based on this understanding, the correct option is:

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