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 as it increases annually at a rate of 22%, we can use the exponential function:
P(t) = P(0)*(1 + r)^t
Where:
P(t) = population after t years
P(0) = initial population (175 in this case)
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 will be:
P(5) = 175*(1 + 0.22)^5
P(5) = 175*(1.22)^5
P(5) ≈ 537.75
Therefore, the approximate population of quail after 5 years will be around 538.