Question

A population of 200 animals is decreasing by 4% per year. At this rate, in how many years will the population be less than 170?

Answer 1

The population will be less that 170 in 4 years

Answer 2

In the question , it is given that the population is decreasing by 4% per year .

So we have to use the following formula of exponential decay:

$P(t) = P_{0} (1-r)^t$

Substituting the given values, we will get

$170 = 200(1-0.04)^t$

Dividing both sides by 200

$\frac{170}{200} = (0.96)^t$

Taking log on both sides

$log (\frac{170}{200}) =log (0.96)^t$

$log (\frac{170}{200}) =t*log (0.96)$

Dividing both sides by log(0.96)

$\frac{ log (\frac{170}{200}) }{log(0.96) } =t$

t = approx 4 years

So after 4 years , the population will be less than 170.