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.

Question

GPT-4o mini · Answer

To analyze the situation described in the equation $ a(t) = 5000(1.12)^t $, we should note that this is an exponential growth function. In exponential growth, the value increases more rapidly over time as $ t $ increases.

At first, the increase may appear moderate, but as the years go by and $ t $ continues to increase, the growth rate accelerates due to the compounding effect of the interest.

Therefore:

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

This statement accurately describes the behavior of the function.

So, the correct answer is Option #1.