Question

Suppose that poaching reduces the population of an endangered animal by 8% per year. Further suppose that when the population of this animal falls below 20, its extinction is inevitable. If the current population of the animal is 1400, when will it face extinction?

Answer 1

`51\text{ years}`

Step-by-step explanation:

Firstly, we need to write an equation that represents this

We have this as:

`P=I(1-r)^n`

Where P is the final population which is given as less than 20

I is the present population

r is the reduction rate which is 8% = 8/100 = 0.08

n is the number of years which is what we want to calculate

Thus, we can have the equation written as:

`\begin{gathered} 1400(1-0.08)^{n\text{ }}\text{ < 20} \\ (0.92)^n\text{ < }(20)/(1400) \\ n\text{ ln 0.92 < ln (}(20)/(1400)) \\ \\ n\text{ < 51} \end{gathered}`

What this mean is that it will take around 51 years for us to have an extinction