a population of 100 frogs increase at an annual rate of 22%.how many frogs will be in 5 years?

Question

a population of 100 frogs in crease at an annual rate of 22%.how many frogs will be in 5 years?

Answer 1

P(t) = 100(1.22)^5 = 270 rounded to the nearest whole frog.

Answer 2

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:

 

x_{n = ar^n-1}

 

where x_n = 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:

 

x_{n = (100)(1.22)⁵}

x_{n = (100)(2.7027)}

x_{n = 270.3}

 

Therefore, the value after 5 years is $270.27