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? show all steps
To write the exponential function to model the quail population, we can use the formula:
P(t) = P_0 * (1 + r)^t
where:
P(t) = population after t years
P_0 = initial population
r = growth rate
t = number of years
Given:
P_0 = 745
r = 16% or 0.16
Therefore, the exponential function to model the quail population is:
P(t) = 745 * (1 + 0.16)^t
After 4 years, the population can be found by plugging t = 4 into the equation:
P(4) = 745 * (1 + 0.16)^4
P(4) = 745 * (1.16)^4
P(4) = 745 * 1.83583936
P(4) ≈ 1,369.17
Therefore, the approximate population after 4 years will be approximately 1,369 quail.