A population of 100 frogs grow at an annual rate of 22% how many frogs will there be in 5 years? In 10 years%

Question

. Not sure how to set up or solve

Answer 1

P(t) = 100(1+0.22)^t is the exponential growth formula (with growth at 22% rate per year) giving population t years after the initial population count is 100.

 

Compute with t = 5 (this is called P(5)) and with t = 10 to get the two answers that you seek.  Calculation duty is left to you.

Answer 2

First let's represent the 100 frogs as "P" meaning present value.

Since there's an annual rate of 22%, next year the value would be "P + 0.22P" which is also equal to "1.22P".

 

Then the next year the value would be "1.22P + 0.22(1.22P)" which can alse be written as "1.22(P+0.22P)" and also as 1.22(1.22P).

 

And this will go on and on, as you continue the years. But you can observe that 1.22 is repeating which is "1 + rate(0.22)".

 

Observing the examples:

In the first year = 1.22P

In the second year = (1.22^2)P

In the third year = (1.22^3)P and so on

 

Therefore the formula for future population of the from is F = P(1+rate)^n; P is the present value and n is the number of years. This is actually the formula of a simple interest that you will be using in the future.