I need help in finding the doubling time for a city whose population is growing by 21% per year

Question

the doubling time is ____ years?

 

So far I have ln2=t(ln(1.21)) but after solving that i get 3.63 and when i log it into my computer it says its wrong. can someone help break down the equation i have or if it is wrong.

Answer 1

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

You can solve this one using the exponential growth formula. That allows you to find the exact doubling time using the equation

Td = ln(2) / ln(1 + r)

On this one we have r = 21% = 0.21, meaning that the equation becomes

Td = ln(2) / ln(1 + 0.21)

=ln(2) / ln(1.21) = 3.64 years

So the doubling time for the city’s population in this scenario is 3.64 years

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 :)

Answer 2

use a calculator & do NOT round off until the end.  thus, the answer is log 2 / log 1.21 = 3.63627... and then you'll get a correct answer, rounding as directed (we don't know how many decimal places your compter system wants).

Answer 3

Hi, Ashley -

 

The answer can be found using the growth equation:

 

x_t = x₀ (1 + r)^t

 

where x_t = the value at time t

          x₀ = the initial value

          r = the growth rate at time t

Rearranging this equation, gives:

 

xt/x0 = (1 + r)t

 

(t) [log(1 + r)] = log (xt/x0)

 

t =  [log (xt/x0)]/[log (1 + r)]

 

For this problem, xt/x0 = 2, r = 0.21 

 

t = log (2) / log (1.21)

 

t = 0.301/0.0828

 

t = 3.63 yrs

 

I believe your answer is correct.