Rate PRoblems

Question

Consider a local community of a prairie dogs in South Dakota that are increasing at a rate of 13% per month. Using the Rule of 70, answer the following:

What is the approximate number of months in which the prairie dog population doubles?

(Round to the nearest tenth.)

 How many months would it take to see the prairie dog population quadruple?

(Round to the nearest tenth.)

Answer 1

here the popoulation is increasing at 13% per month compounding every month.

So, by rule of 70,  number of months needed to double =70/rate = 70/13 ~ 5.4 months.

 

number of months to quadraple = 5.4 *2 = 10.8 months

Answer 2

1. The rule of 70 says that the growth rate in % per some amount of time, times the number of periods of that amount of time, equals approximately 70.

For example, if a bank account is giving around 1% annual interest per year, it would take around 70 years for the money in the account to double.

So in this case, the population growth rate is 13% per month. To find the number of months it would take for the population to double, divide 70 by 13. The result is approximately 5.38 so the answer to the nearest tenth is 5.4 months.

 

2.  What does quadruple really mean?  It means double and then double again.  So it would take twice as many months to quadruple as it does to double.  That means around 10.8 months.