If a population grows at 2% per year, approximately how many years to double according to Rule of 70?

If a population grows at 2% per year, approximately how many years to double according to Rule of 70?

• A. 35 years
• B. 70 years
• C. 140 years
• D. 7 years

Answer: (A)

The key idea here is the Rule of 70, a quick way to estimate how long it takes for a quantity growing at a steady annual percentage to double. Doubling time ≈ 70 divided by the growth rate in percent. At 2% per year, that gives about 70 / 2 = 35 years. For a quick check with the exact formula, imagine the population grows as P(t) = P0 × (1.02)^t. Set this equal to 2P0 to double: (1.02)^t = 2. Taking logs, t = ln(2) / ln(1.02) ≈ 0.6931 / 0.0198 ≈ 35 years. So the Rule of 70 gives a close, reliable estimate for this small growth rate. Why the other options don’t fit: 70 years would correspond to roughly 1% growth per year, 140 years to about 0.5% growth, and 7 years to around 10% growth.

The key idea here is the Rule of 70, a quick way to estimate how long it takes for a quantity growing at a steady annual percentage to double. Doubling time ≈ 70 divided by the growth rate in percent. At 2% per year, that gives about 70 / 2 = 35 years.

For a quick check with the exact formula, imagine the population grows as P(t) = P0 × (1.02)^t. Set this equal to 2P0 to double: (1.02)^t = 2. Taking logs, t = ln(2) / ln(1.02) ≈ 0.6931 / 0.0198 ≈ 35 years. So the Rule of 70 gives a close, reliable estimate for this small growth rate.

Why the other options don’t fit: 70 years would correspond to roughly 1% growth per year, 140 years to about 0.5% growth, and 7 years to around 10% growth.