A town's population is predicted to increase by 4% every n months. If the growth is modeled by the expression P(1.04)^ frac t 12 where t is in months, what is the value of n?

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TAS Mathematics QUESTION #5391

Question 1

A town's population is predicted to increase by $4\%$ every $n$ months. If the growth is modeled by the expression $P(1.04)^{\frac{t}{12}}$ where $t$ is in months, what is the value of $n$?

$8$
$12$✔️
$18$
$72$

Correct Answer Explanation

In exponential growth $A = P(1+r)^{\frac{t}{n}}$, the denominator $n$ represents the period of time required for the growth $r$ to occur. Here $n=12$.

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