Question

several years ago wolves were reintroduced in to a national park in north carolina in north carolina. Researchers have monitored the populations over the last severals years and the per capita growth rate of the population is .5. If the current population size is 100, what equation would you use to determine how large the population will be in ten years

Answer 1

Answer:
`5766.503\ \text{wolves}`

Explanation:

Given

Current Population of wolves is
`P_o=100`

If the growth rate is
`=0.5`

So the population in next year is

`P_1=100+100* 0.5`

`P_1=100(1+0.5)`

similarly
`P_2=100(1+0.5)^2`

So population after n years is
`P_n=P_o(1+r)^n`

Population after 10 years is

`P_(10)=100(1+0.5)^(10)`

`P_(10)=5766.503\ \text{wolves}`