Question

an initial population of 745 quail increases at an anual rate of 16%. write an exponential function to model the population. what is the population after 4 years.

Answer 1

@mathstudent55

Answer 2

\[\large P(t)=P_{0}(1.16)^{t}\]
Plugging in the given values we get:
\[\large P(4)=745(1.16)^{4}=1349\ quail\]

Answer 3

huh okay. can you explain how you did that so i can understand?

Answer 4

Each year the population increases by 16%. Therefore if we multiply the population at the start of the year by 1.16 we find the population at the end of the year. So at the end of the first year the population is 745 * 1.16, at the end of the second year the population is (745 * 1.16) * 1.16, at the end of the third year the population is (745 * 1.16 * 1.16) * 1.16 and at the end of the fourth year the population is:
\[\large 745\times 1.16\times1.16\times 1.16\times 1.16=745(1.16)^{4}\]