An increasing curve with an arrow on the upper end is plotted on a coordinate plane. The x-axis is labeled time left parenthesis years right parenthesis. The y-axis is labeled amount left parenthesis dollars right parenthesis.
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.
1 answer
The function given, \( a(t) = 5,000(1.12)^t \), represents exponential growth. In such a model, as time \( t \) increases, the amount \( a(t) \) grows slowly at first, but as \( t \) continues to increase, the growth rate accelerates, and the amount begins to increase more quickly.
Therefore, the correct answer is:
Option #1: As t increases, a increases slowly at first and then quickly.
