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.
b. 525 is the population of the frogs after 5 years
Frog number = 250(1.22)^n , where n is the number of years
after 5 years --- > 250(1.22)^5 = appr. 676 frogs
a=250(.22)
a. To write an exponential function to model the population of frogs, we need to understand that an exponential growth model can be represented by the formula:
P(t) = P0 * (1 + r)^t
Where:
- P(t) is the population at time t
- P0 is the initial population (at time t = 0)
- r is the annual growth rate in decimal form (22% is 0.22)
- t is the time in years
In this case, the initial population (P0) is 250 frogs, and the annual growth rate (r) is 22% or 0.22.
So, the exponential function that models the population of frogs would be:
P(t) = 250 * (1 + 0.22)^t
b. To find the population of frogs after 5 years, substitute t = 5 into the exponential function:
P(5) = 250 * (1 + 0.22)^5
Now, calculate the value:
P(5) = 250 * (1.22)^5
P(5) ≈ 250 * 1.869
P(5) ≈ 467.25
Therefore, the population of frogs after 5 years would be approximately 467 frogs.