An initial population of 745 quail increases at an annual rate of 16%. Write an exponential function to model the quail population. What will the approximate population be after 4 years?

Answer 1

An exponential function that models this situation can be written as:

P(t) = P₀ * (1 + r)^t

Where P(t) is the population after time t, P₀ is the initial population, r is the rate of increase as a decimal, and t is the time in years.

In this case, P₀ = 745, r = 0.16 (16% written as a decimal), and t = 4.

Plugging these values into the equation, we have:

P(4) = 745 * (1 + 0.16)^4

Calculating this, we get:

P(4) ≈ 863.005

Therefore, the approximate population after 4 years would be 863 quail.