What is the doubling time for a population if the growth percentage is 2.5 percent?

Question

a. .035 years

b. 1.75 years

c. 28 years

d. 72.5 years

e. 175 years

Answer 1

28 years

(Use the "rule of 70" to calculate approximate doubling times. 70 divided by 2.5 = 28)

Answer 2

As there is no correct answer yet, I shall give it a try. As the population grows with 2.5 percent, that means that every 2,5 year a new child is born. If you take into account, that one woman can bear more than one child (as no mother can have 2.5 children), it will be ten children more after ten years per mother.

As your question does not say how many mothers there are, I came to the conclusion that it must be a trick question and cannot be answered.  

Answer 3

You can solve this similar to a simple (or compound) interest problem.  You don't mention the period in which the population grows by 2.5%, but the answers make it seem like it is once per year.

Equation:  x(1 +  r)^t = 2x

x is population, t is time, r is the rate(percent),  ^ is notation for “to the power of”

x(1 + .025)^t = 2x

x(1.025)^t= 2x    

1.025^t = 2  (divide by x)

t log 1.025 = log 2   (multiply by log)

t = log 2 / log 1.025

t = 28.07   (so about  28 years)

If the population increases multiple times per year, you’d want to use x(1 +  r/n)^(nt) = 2x, where n is the # of times it increases per year.