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‰ˆ 391.256

Therefore, the quail population after 4 years will be approximately 391 quails.