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.