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)

Question

GPT-4o mini · Answer

The function $ a(t) = 5,000(1.12)^t $ represents an exponential growth model because the growth rate is constant at 12%. In an exponential growth function, when plotted on a graph: - Initially, for small values of $ t $, the increase in the value of $ a(t) $ is relatively slow. - However, as $ t $ increases, the value of $ a(t) $ starts to grow more rapidly due to the compounding effect. So the correct interpretation of the graph is that as $ t $ increases, $ a $ increases slowly at first and then quickly. Therefore, the correct statement is **Option #1: As t increases, a increases slowly at first and then quickly.**