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?
An exponential function that models this situation can be written as:
P(t) = Pā * (1 + r)^t
Where P(t) is the population after time t, Pā is the initial population, r is the rate of increase as a decimal, and t is the time in years.
In this case, Pā = 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) ā 863.005
Therefore, the approximate population after 4 years would be 863 quail.