Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.%0D%0A%0D%0AAn 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?
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To write an exponential function to model the quail population, we can use the general form of an exponential function:
P(t) = P0 * (1 + r)^t
Where:
- P(t) is the population at time t
- P0 is the initial population
- r is the growth rate as a decimal
- t is the number of years
In this case, the initial population (P0) is 745 quail and the growth rate (r) is 16% per year, or 0.16 as a decimal. Let's plug these values into the formula:
P(t) = 745 * (1 + 0.16)^t
Now, to find the approximate population after 4 years, we need to substitute t = 4 into the formula:
P(4) = 745 * (1 + 0.16)^4
Calculating this expression:
P(4) = 745 * (1.16)^4
P(4) = 745 * 1.75987584
P(4) ≈ 1310.8534
Thus, the approximate population after 4 years is 1310 quail.