growth question

Question

 A population of 20 deer are introduced into a wildlife sanctuary. It is estimated that the sanctuary can sustain up to 400 deer. Absent constraints, the population would grow by 80% per year.

how many after one year

how many after two years



Answer 1

This is similar to compound interest where the amount A after t years, starting from an initial value P and growing at a rate r (converted from percent to decimal) is: A = P(1+r)^t. After one year we have A = 20(1+0.80)¹ = 36 deer. After two years A = 20(1.8)² = about 65 deer (you want to round off what the calculator says to the nearest whole animal!).