Table of Contents

• Section 1. Exact Doubling Time
• 1: In search of ... the exact doubling time
• 2: Finding doubling time with messy numbers
• 3: Logs = Exponent-busters
• 4: Let's bust some exponents
• 5: More exponent busting
• Section 2. Applications
• 6: World Population
• 7: Growth of technology
• 8: Extended Problem: How long DOES poor Frank have?
• 9: Review

Review

In order to find the exact doubling time, you first need to understand how to use logs to get rid of exponents. In short,

logs knock exponents down to multiplication, and

logs knock multiplication down to addition.

You need to know this, because the number of doublings (t) is the exponent in the exponential growth equation:

N_t = N₀ 2^t

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 through 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. And finally, poor Frank knows just how fast his meningitis is progressing...