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8-111.

THE RULE OF 70

The Rule of 70 is a useful rule of thumb for determining the doubling time under steady (exponential) growth. To get the doubling time, the rule tells us to divide 70 by the growth rate, expressed as a percentage. Carry out the following steps to see why the Rule of 70 works as it does.

Use

withto find the exact doubling timein terms of the growth ratewithout using your calculator. In other words expressin terms of.If

is the rate of growth (i.e.), and is the percentage rate of growth (i.e.), express in terms of.Using your calculator to evaluate

, show that doubling time with growth rate is . is closer to than . Why do we use ? We use

because it makes the mental arithmetic easier.