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

The function given is $ a(t) = 5000(1.12)^t $, which is an exponential growth function. In general, exponential functions of the form $ a(t) = a_0(1 + r)^t $ (where $ r > 0 $) will show a characteristic behavior: - They increase slowly at first when $ t $ is small because the factor $ (1.12)^t $ is still relatively small. - As $ t $ increases, the exponential term grows rapidly, causing the overall function $ a(t) $ to increase more quickly. Given these characteristics, the correct statement about the graph of the function is: **Option #1: As t increases, a increases slowly at first and then quickly.**