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Use the information in the table to calculate Growtopia's average annual growth rate for real GDP and the approximate amount of time it would take for Growtopia's real GDP to double.
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12. Productivity and Economic Growth
Growth Rates and the Rule of 70
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What is the rule of 70?
A
An approximation to estimate the doubling time (in years) of a variable by dividing 70 by its annual percentage growth rate.
B
A claim that an economy's GDP will double every 70 years regardless of its growth rate.
C
A rule that estimates the time to increase a variable by 70% by dividing 70 by the annual growth rate.
D
A precise formula for doubling time using natural logs (T = ln 2 / growth rate), not an approximation.
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Understand that the Rule of 70 is a simple way to estimate how long it takes for a variable, such as GDP or population, to double given a constant annual growth rate.
Recall the formula for the Rule of 70: the doubling time (in years) is approximately equal to \(\frac{70}{\text{annual growth rate (in %)}}\).
Recognize that this is an approximation, not an exact calculation, and it works well for growth rates that are not too large.
Compare this to the exact doubling time formula using natural logarithms: \(T = \frac{\ln 2}{\text{growth rate (in decimal form)}}\), where \(\ln 2 \approx 0.693\).
Conclude that the Rule of 70 provides a quick mental calculation to estimate doubling time, making it a useful tool in macroeconomics for understanding growth dynamics.
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