Question

A native wolf species has been reintroduced into a national forest. Originally 200 wolves were transplanted. After 3 years, the population had grown to 270 wolves. If the population grows exponentially, how many wolves will be there in 10 years

Answer 1

we can find the value of 1.35

270=200(1+r)

where r is the common ratio of each term

we need to clear r

`(1+r)=(270)/(200)`
`r=1.35-1`

`r=.35`

to find this formula exponentially

we use

PW=P0(1+r)^n

the formula can we use for this problem will be

`PW=P0\mleft(1.35\mright)^n`

where

PW is the new population of wolves

P0 the original population of wolves

n=the years

`PW=200(1.35)^(10)=4021`

4021 wolves will be there in 10 years