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

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.

Answer 1

Option #2: As t increases, a increases quickly at first and then slowly. This is because the function a(t) = 5,000(1.12)^t is an exponential function with a growth rate of 12%. As t increases, the power of (1.12)^t increases, causing the value of a(t) to increase rapidly at first. However, as t continues to increase, the growth rate slows down and a(t) increases at a slower pace.