An initial population of 175 quail increases at an annual rate of 22%. Write an exponential function to model the quail population. What will the approximate population be after 5 years?
To model the quail population, we can use the exponential growth formula:
P(t) = P0 * (1 + r)^t
Where:
P(t) = the population after t years
P0 = the initial population (175 quail)
r = annual growth rate (22% or 0.22)
t = number of years
Plugging in the values, we get:
P(t) = 175 * (1 + 0.22)^t
After 5 years, the population would be:
P(5) = 175 * (1 + 0.22)^5
P(5) = 175 * (1.22)^5
P(5) = 175 * 2.38876
P(5) ≈ 418.13
Therefore, the approximate quail population after 5 years would be 418 quail.