# 9: Summary

In order to find the exact doubling time, you first need to understand how to use logs to get rid of exponents.  You need to know this, because the number of doublings (n) is the exponent in the exponential growth equation:

Nt = N0 2n

So, to determine the exact doubling time of a population, you need a two-step procedure:

1. Substitute the two population sizes into the equation, then divide both sides of the equation by N0, and finally take the log of both sides. This gives you the number of doublings.
2. Divide the amount of time passed by the number of doublings to find the doubling time.

This same procedure works on any kind of exponential growth, as we saw in examples about world population and about the growth of technology.

## Learning Outcomes

Now that you have completed this module, you should be able to:

• Use the growth equation to calculate generation time from a set of data
• Know how to use logarithms (logs) to solve equations with exponents

If you want a printer-friendly version of this module, you can find it here in a PDF document. This printer-friendly version should be used only to review, as it does not contain any of the interactive material, and only a skeletal version of problems solved in the module.