Question

Please help!!

Write an exponential function to model the situation. Then estimate the value of the function after 5 years (to the nearest whole number).
A population of 290 animals that increases at an annual rate of 9%.

Answer 1

The estimated population after 5 years is approximately 413 animals.

Step-by-step explanation:

To model the situation, we can use the formula for exponential growth:
`P(t) = P0(1 + r)^t,` where P(t) is the population after t years, P0 is the initial population, r is the annual growth rate, and t is the number of years.

In this case, the initial population is 290 animals and the annual growth rate is 9%, which can be expressed as 0.09.

The function becomes:
`P(t) = 290(1 + 0.09)^t`.

To estimate the value of the function after 5 years, we substitute t = 5 into the formula and calculate:

`P(5) = 290(1 + 0.09)^5`

`= 290(1.09)^5`

= 413.

Therefore, the estimated population after 5 years is approximately 413 animals.

Answer 2

421 because 9% of 290 is 26.1 so you multiply that by 5 and add 290 and you get 420.5 so you get 421 rounded to the nearest whole number