# Doubling and Tripling Time Calculator

You can use this doubling and tripling time calculator to determine the time it will take for a quantity to double and triple in value (or size) at a predetermined constant growth rate.

Doubling & Tripling Time Calculator

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## Reference

The exponential function can be employed when a given quantity grows at a constant rate of increase

y(t) = agt ,

where a is the original quantity at time t = 0 and g represents the growth factor. For instance, if we have a population of 50 people that grows at a rate of 10% every year, we have the following:

y(t) = 50(1.1)t

At a growth rate of r%, the growth factor will be g = (1+r/100). If you would like to identify the doubling or tripling time of the population, you would only need to determine the value of g or r.

## Determining the doubling time

To identify the doubling time for a given process, there is a requirement to solve the equation 2a = agt for t. If both sides are divided by a, we have 2 = gt. If the natural logarithm of both sides is taken and t is isolated, we have the following:

t = LN(2)/LN(g),

t = LN(2)/LN(1+r/100)

Example: If a savings account exponentially grows at a rate of 2.5% per year, the doubling time will be as follows:

LN(2)/LN(1+2.5/100) = 28.071 years, or approximately 28 years, 9 months.

## Determining the tripling time

To identify the tripling time for a given process, there is a requirement to solve the equation 3a = agt for t. Again, if both sides are divided by a, we will have 3 = gt. If the natural logarithm of both sides is then taken and we isolate t, we have the following:

t = LN(3)/LN(g),

t = LN(3)/LN(1+r/100)

Example: If a population of bacteria exponentially grows at a rate of 5% per day, the tripling time will be as follows:

LN(3)/LN(1+5/100) = 22.517 days, or approximately 22 days 12 hours, 24 minutes.