A population of 298 quail increases at an annual rate of 8%. write an exponential function to model the quail population. What will the population be after 4 years? explain
To model the quail population using an exponential function, we can use the formula:
P(t) = Pā * (1 + r)^t
Where:
P(t) is the population at time t
Pā is the initial population
r is the annual growth rate as a decimal
t is the number of years
In this case, the initial population is 298 and the annual growth rate is 8% or 0.08.
Therefore, the exponential function to model the quail population is:
P(t) = 298 * (1 + 0.08)^t
To find the population after 4 years, we substitute t = 4 into the function:
P(4) = 298 * (1 + 0.08)^4
P(4) = 298 * (1.08)^4
Calculating this, we find:
P(4) ā 391.256
Therefore, the quail population after 4 years will be approximately 391 quails.