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

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

Answer 1

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

Reason: a(t)=5000(1.12)^t is exponential growth (base > 1). Early increases are small in absolute terms, but because growth is proportional to the current amount, the absolute increases accelerate over time (the graph is increasing and concave up).