Supoose a community of rabbits begins with a population of 100 and grows 6% each year.

Question

Determine the doubling time using the rule of 70. State your answer to the nearest 0.01 years.

Determine the doubling time using the formula for the exact doubling time.

Answer 1

By the rule of 70, the doubling time = 70/6 or 11.67 years.

 

To find the exact doubling time:

 

N(t) = N(0) x e^rt

 

from which

 

t = ln [ N(t)/N(0) ] / r

 

In this case, N(t)/N(0) = 200/100 = 2 so that

 

t = ln(2)/r = 0.693/0.6 = 11.55 years

Answer 2

Hello, thank you for taking the time to post your question!

For the rule of 70 you would just take

Doubling Time = 70 / Annual Growth Rate

For this scenario that means taking

Doubling Time = 70 / 6 = 11.67

Meaning that it would take about 11.67 years for the population to double based on the Rule of 70 estimation.

For the exact formula you want to use

Doubling Time = ln(2) / r , as derived from the exponential growth model. For this one that means

ln(2) / 0.06 = 11.5524

Meaning that it would take 11.55 years for the population to double

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)