An initial population of 298 quail increases at an annual rate of 8%. Write an exponential function to model the quail population. What will the approximate population be after 3 years?
To model the quail population with an exponential function, we can use the formula:
P(t) = Pā * (1 + r)^t
where:
P(t) = population after t years
Pā = initial population
r = annual growth rate
t = number of years
In this case:
Pā = 298
r = 8% = 0.08
t = 3
Therefore, the exponential function to model the quail population is:
P(t) = 298 * (1 + 0.08)^3
P(t) = 298 * (1.08)^3
P(t) = 298 * 1.259712
P(t) ā 375.56
Therefore, the approximate population of quail after 3 years will be around 375.56.