Question

An initial population of 78 rare animals is growing at an animal reservation at a rate of 17% per year. Write an expression to model how many animals there will be in 3 years.

Answer 1

78(1.17)^3
= 124.926

Answer 2

Let P be the initial population of 78 rare animals, and r be the rate of growth, which is 17% or 0.17 in decimal form. We can use the formula for exponential growth to model the population of animals after t years:

P(t) = P * (1 + r)^t

Substituting the given values, we get:

P(t) = 78 * (1 + 0.17)^t

To find the population after 3 years, we can plug in t = 3:

P(3) = 78 * (1 + 0.17)^3

Simplifying the expression, we get:

P(3) = 78 * (1.17)^3

P(3) ≈ 125.32

Therefore, there will be approximately 125 rare animals in the reservation after 3 years, assuming the growth rate remains constant at 17% per year.