Question

A population of a certain species of marsupial is 12,000 animals and is increasing at the rate of 9% annually.Write an equation for y, the population at time t (in years), representing the situation.y =How many marsupials are in the population after 7 years?

Answer 1

Given:

Initial population = 12,000

Rate of increasing = 9% = 0.09

Required: Population after 7 years

Step-by-step explanation:

The population growth after t years is defined as

`P(t)=P_0e^(kt)`

Substitute the given values into the formula.

`P(t)=12000e^(0.09t)`

To find the population after 7 years, substitute 7 for t in P(t).

`\begin{gathered} P(7)=12000e^(0.09\cdot7) \\ \approx22531 \end{gathered}`

Final Answer: 22531 marsupials are there after 7 years