Question

Use the image to answer the 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)^t
, where a is the amount after t years. Which one of the following statements is true about the graph of the function?

(1 point)
Responses

As t increases, a increases quickly at first and then slowly.
As t increases, a increases quickly at first and then slowly .

As t increases, a increases slowly at first and then quickly.
As t increases, a increases slowly at first and then quickly .

As t increases, a decreases slowly at first and then quickly.
As t increases, a decreases slowly at first and then quickly .

As t increases, a decreases quickly at first and then slowly.
As t increases, a decreases quickly at first and then slowly .
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Answer 1

The situation described involves exponential growth, as modeled by the function \( a(t) = 5000(1.12)^t \). In such a model, the amount \( a \) increases over time, and typically, it increases slowly at first and then more rapidly as time progresses, due to the compounding effect of the growth rate.

Therefore, the true statement about the graph of the function is:

**As t increases, a increases slowly at first and then quickly.**