Question

Enter your answer and show all the steps that you use to solve this problem in the space provided.

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?

(2 points)

Answer 1

To write an exponential function to model the quail population, we can use the formula for exponential growth:

\[P(t) = P_0 * (1 + r)^t\]

Where:
- \(P(t)\) is the population after \(t\) years
- \(P_0\) is the initial population (745 quail)
- \(r\) is the annual growth rate (16% or 0.16)
- \(t\) is the time in years

Plugging in the values, we get:

\[P(t) = 745 * (1 + 0.16)^t\]

\[P(t) = 745 * 1.16^t\]

Therefore, the exponential function to model the quail population is \(P(t) = 745 * 1.16^t\).

To find the approximate population after 4 years, we can plug in \(t = 4\) into the function:

\[P(4) = 745 * 1.16^4\]

\[P(4) = 745 * 1.8607\]

\[P(4) \approx 1390.48\]

After 4 years, the approximate quail population will be 1390 quail.