Question

a population of 100 frogs increases at an annual rate of 22% how many frogs will there be in 10 years

Answer 1

Because the number of frogs is increasing by the same ratio each year, this problem can be solved by the equation for a geometric progression. That equation is shown below:

xn = arn-1

where xn = the value of x after n terms
a = the initial value
r = the ratio of each term to the one before it (e.g. x2/x1)

For this case, we are starting with an initial value (a) of 100. After that there will be 5 more terms in the progression representing the value after each of the 5 years. So there are a total of 6 terms in the progression meaning that n= 6.

The ratio (r) which is the amount being multiplied each year is 1.22 because the rate is increasing by 22% each year.

Plugging these values for a, n, and r into the equation above gives:

xn = (100)(1.22)5
xn = (100)(2.7027)
xn = 270.3

Therefore, the value after 5 years is $270.27