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

, 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.
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Answer 1

To analyze the function \( a(t) = 5,000(1.12)^t \), we need to consider how exponential growth behaves.

1. Initial Behavior: When \( t \) is small, the value of \( (1.12)^t \) is close to 1. Therefore, the amount \( a(t) \) starts off growing slowly.
2. Long-Term Behavior: As \( t \) increases, \( (1.12)^t \) increases exponentially. This means that after some time, the growth rate accelerates, causing \( a(t) \) to increase more rapidly.

Thus, the correct statement about the graph of the function is:

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

So, the answer is Option #1.