Write an exponential function to model the situation. Then predict the value of the function after 5 years (to the nearest whole number). A population of 210 animals that increases at an annual rae of 19%

Can you explain your answer please?

number(t) = 210(1.19)^t

number(5) = 210(1.19)^5 = appr 501

To model the situation of a population of animals increasing at a rate of 19% annually, we can use the formula for exponential growth:

P = P0 * (1 + r)^t

Where:
P is the final population size
P0 is the initial population size
r is the growth rate expressed as a decimal
t is the time period in years

In this case, P0 (initial population) is 210, and the growth rate (r) is 19% or 0.19. Let's calculate the population after 5 years using this formula:

P = 210 * (1 + 0.19)^5

Simplifying the equation:

P = 210 * (1.19)^5

Calculating:

P ≈ 210 * 2.89

P ≈ 607.92

Rounding to the nearest whole number, the population after 5 years is predicted to be approximately 608 animals.