Question

the population of mathlandia in 2015 was 23,473 and was projected to decay at a rate of 12% per year. which of the following functions represents the population after t years

Answer 1

Since the population was projected to decay, then it means the number will be dropping over the years

Hence the formula to use will be;

$\begin{gathered} P(t)=a(1-r)^t \\ \text{where a is the initial population in 2015} \\ r\text{ is the rate of decay per year} \\ t\text{ is the number of years} \\ \end{gathered}$

Hence;

$\begin{gathered} P(t)=23473(1-\frac{12}{100})^t \\ P(t)=23473(0.88)^t \end{gathered}$

Hence the correct answer is option B.