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

`image`

Dividing both sides by 200

`(170)/(200) = (0.96)^t`

Taking log on both sides

`log ((170)/(200)) =log (0.96)^t`

`log ((170)/(200)) =t*log (0.96)`

Dividing both sides by log(0.96)

`( log ((170)/(200)) )/(log(0.96) ) =t`

t = approx 4 years

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