Question

Suppose that poaching reduces the population of an endangered animal by

Answer 1

Answer:

38.26 years.

Step-by-step explanation:  

We have been given that the population of an endangered animal by  reduces 8​% per year. the current population of the animal is  1700. When the population of this animal falls below  70​, its extinction is inevitable.  

Let us write the model for population of this animal (y) after x years.

Since we know that an exponential decay function is in form: $y=a*(1-r)^x$, where,

a= Initial value.

r = Rate in decimal form.

Let us convert our given rate in decimal form.

$8\%=\frac{8}{100}=0.08$

Upon substituting a= 1700 and r = 0.08 in exponential function, we will get the model of animal population as:

$y=1700*(1-0.08)^x$

$y=1700*(0.92)^x$

Let us find, when the animal population will face extinction by substituting y=70 in our function.

$70=1700*(0.92)^x$  

$\frac{70}{1700}=\frac{1700*(0.92)^x}{1700}$

$0.0411764705882353=0.92^x$  

Let us take natural log of both sides of our equation.

$ln(0.0411764705882353)=ln(0.92^x)$

$ln(0.0411764705882353)=x*ln(0.92)$

$-3.1898882879949483163=x*-0.0833816089390511$

$x=\frac{-3.1898882879949483163}{-0.0833816089390511}$

$x=38.2564971890460849445284\approx 38.26$

Therefore, the population of the animal will face extinction after 38.26 years.