A population of 250 frogs increases at an annual rate of 22%.
a. Write an exponential function to model the population of frogs.
b. Find the population of frogs after 5 years.
To write an exponential function to model the population of frogs, we need to use the formula for exponential growth, which is:
P = P0 * (1 + r)^n
Where:
P = Final population
P0 = Initial population
r = Growth rate
n = Number of time periods
In this case, we have:
P0 = 250 (initial population)
r = 22% (growth rate, which can also be expressed as 0.22)
n = 1 (since the annual rate refers to one year)
Substituting these values into the formula, we get:
P = 250 * (1 + 0.22)^1
Simplifying the right side of the equation, we have:
P = 250 * (1.22) = 305
Therefore, the exponential function to model the population of frogs is:
P = 250 * (1.22)^n