Scientists estimate the current population of orangutans to be 2500 individuals in a shrinking forest with an estimated maximum capacity of 1500 orangutans. They later found that the orangutan population to have dropped to 2100 individuals in 2 years. Assuming that the population of orangutans satisfies the logistics equation, find an expression for the size of the population after t. How long will it take for the population to shrink to 1800 orangutans?

Given:

Scientists estimate the current population of orangutans to be 2500 individuals in a shrinking forest with an estimated maximum capacity of 1500 orangutans. They later found that the orangutan population to have dropped to 2100 individuals in 2 years.

To Find:

• Assuming that the population of orangutans satisfies the logistics equation, find an expression for the size of the population after t.
• How long will it take for the population to shrink to 1800 orangutans?

Concept:

$$\begin{gathered} \text{The logistic growth model is given by:} \\ P\left(t\right)=\frac{M{P}_0{e}^{rt}}{M+P_0\left(e^{rt}-1\right)}, \text{where} \\ M : \text{maximum capacity} \\ {P}_0 : \text{Initial Population} \\ r :\text{ rate of growth} \end{gathered}$$