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 70​, its extinction is inevitable​ (owing to the lack of reproductive options without severe​ in-breeding). If the current population of the animal is 1400​, when will it face​ extinction?

Answer 1

Answer:  36 years

Step-by-step explanation:

Here, the current population of the animal is 1400​,

And, the  population of an endangered animal by 8​% per year.

Also, Further suppose that when the population of this animal falls below 70​, its extinction is inevitable​.

Let after x years the population of animal falls below 70,

Therefore, $1400(1-\frac{8}{100} )^x < 70$

⇒ $(\frac{92}{100})^x < \frac{70}{1400}$

⇒ $(\frac{92}{100})^x < \frac{1}{20}$

⇒ $x log(.92) < log(0.5)$

⇒$- 0.03621217265 x < -1.30102999566$

⇒x>35.9279739462

Thus, after 36 years( Approx) the population of the animal will be fall towards 70.