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?

Answer 1

To model the quail population with an exponential function, we can use the formula:

P(t) = P₀ * (1 + r)^t

where:
P(t) = population after t years
P₀ = initial population
r = annual growth rate
t = number of years

In this case:
P₀ = 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) ≈ 375.56

Therefore, the approximate population of quail after 3 years will be around 375.56.