The country of Lower Skipjack has been experiencing economic growth of 3.5%. If the growth continues at this rate, how many years will it take for the economy to double in size?

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BlackTom AI · Accepted Answer

The question asks how long it would take for the economy to double at a steady growth rate of 3.5% per year.
First, recall the rule of 70 (an approximate method for doubling time): doubling time ≈ 70 divided by the annual growth rate expressed as a percentage.
Option 1: 35 years would correspond to a growth rate of about 70/35 = 2%. Since the given rate is 3.5%, 35 years is too long for a doubling.
Option 2: 245 years would imply 70/245 ≈ 0.2857% annual growth, which is far smaller than 3.5%. This is inconsistent with the stated rate.
Option 3: 20 years aligns with the rule of 70 as 70/3.5 = 20. A growth rate of 3.5% indeed yields a doubling time close to 20 years, so this option matches the given information.
Option 4: 70 years would require a growth rate of about 1% per year (70/70 = 1%). Since the rate is 3.5%, this option underestimates the speed of growth and results in a longer doubling time than actually would occur.
In summary, each incorrect option corresponds to a different implied growth rate when applying the rule of 70, and only the one with 20 years is consistent with a 3.5% growth rate. The calculation framework here hinges on converting growth rate into a doubling time using the 70-percentage-point rule, which is a common heuristic in economics and finance.

ECON 2002.01 SP2025 (25230) Final Exam

The country of Lower Skipjack has been experiencing economic growth of 3.5%. If the growth continues at this rate, how many years will it take for the economy to double in size?

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