How to Calculate Doubling Time and Tripling Time
If a quantity is growing at a constant rate of increase, you can model the process with the exponential function
y(t) = ABt,
where A is the initial amount at time t = 0 and B is the growth factor. For example, if a population starts out at 1000 individuals and grows by 5% each year, the equation is
y(t) = 1000(1.05)t.
Given a growth rate of R%, the growth factor is B = 1 + R/100. If you wish to find the doubling time or tripling time of the population, you only need to know the value of B or R.
Doubling TimeTo find the doubling time of a process, you must solve the equation 2A = ABt for t. Dividing both sides by A yields 2 = Bt. If you take the natural logarithm of both sides and isolate t, you arrive at
t = LN(2)/LN(B).
Example: A savings account grows at an annual rate of 3.25%. Since R = 3.25, we have B = 1.0325. Thus, the doubling time is
LN(2)/LN(1.0325) = 21.672 years, or about 21 years and 8 months.
Tripling TimeTo find the tripling time of a growth process, you must solve the equation 3A = ABt for t. Again, dividing both sides by A yields 3 = Bt. And if you take the natural logarithm of both sides and isolate t, you arrive at
t = LN(3)/LN(B).
Example: A bacterial culture grows at a rate of 4.1% per day. In this case, R = 4.1 and B = 1.041. Thus, the tripling time is
LN(3)/LN(1.041) = 27.341 days, or about 27 days 8 hours and 11 minutes.
© Had2Know 2010