Question

Suppose that poaching reduces the population of an endangered animal by 6​% per year. Further suppose that when the population of this animal falls below 20​, its extinction is inevitable​ (owing to the lack of reproductive options without severe​ in-breeding). If the current population of the animal is 1500​, when will it face​ extinction? Comment on the validity of this exponential model.

Answer 1

If poaching reduces the population of an endangered animal by 6% and the criteria of population extinction is 20 with present population 1500 then it will take 3.62 years to reach to the mark of extinction.

Given Poaching reduces the population of endangered animals by 6% per year. The criteria of population extinction is 20. Present population being 1500.

Number of years taken by the population of endangered animals to reach to 20 mark can be calculated as under:

20=1500*$(1-0.06)^{n}$

20=1500*$0.94^{n}$

20/1500=$0.94^{n}$

0.133=$0.94^{n}$

take log both sides

log(0.133)=log$0.94^{n}$-------1

log(0.133)=nlog (0.94)

put the values log values:

log(0.133)=-0.8761

log(0.94)=-0.0268

Taking 1

-0.8761=n*(-0.0268)

n=0.8761/0.0268

n=3.269

Hence to reach level of 20 the population takes 3.2 years.

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