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, [tex]1400(1-\frac{8}{100} )^x < 70[/tex]
⇒ [tex](\frac{92}{100})^x < \frac{70}{1400}[/tex]
⇒ [tex](\frac{92}{100})^x < \frac{1}{20}[/tex]
⇒ [tex]x log(.92) < log(0.5)[/tex]
⇒[tex]- 0.03621217265 x < -1.30102999566[/tex]
⇒x>35.9279739462
Thus, after 36 years( Approx) the population of the animal will be fall towards 70.
