(a) There is a trick, called the Rule of 70, that can beused to get a quick estimate of

Chapter 8, Problem 39

(choose chapter or problem)

(a) There is a trick, called the Rule of 70, that can be used to get a quick estimate of the doubling time or half-life of an exponential model. According to this rule, the doubling time or half-life is roughly 70 divided by the percentage growth or decay rate. For example, we showed in Example 5 that with a continued growth rate of \(1.10 \%\) per year the world population would double every 63 years. This result agrees with the Rule of 70, since \(70 / 1.10 \approx 63.6\). Explain why this rule works.

(b) Use the Rule of 70 to estimate the doubling time of a population that grows exponentially at a rate of \(1 \%\) per year.

(c) Use the Rule of 70 to estimate the half-life of a population that decreases exponentially at a rate of \(3.5 \%\) per hour.

(d) Use the Rule of 70 to estimate the growth rate that would be required for a population growing exponentially to double every 10 years.

Equation Transcription:

1%

3.5%

Text Transcription:

1.10%

70/1.10 almost equal to 63.6

1%

3.5%