In 1500, the population of a region was 1.2 million; by 1800 it grew to 4.5 million. Assuming exponential growth, calculate the annual growth rate (rounded to two decimal places).

Step-by-step solution

1. Compute the population ratio: $\frac{4.5}{1.2}=3.75$.
2. Take the natural logarithm: $\ln 3.75=1.322$.
3. Divide by the time span (300 years): $\frac{1.322}{300}=0.0044067$.
4. Convert to percentage: $0.0044067\times 100=0.44\%$ per annum.
5. Answer: 0.44% per annum.

Concept tested: Population growth rate

Published 4 October 2026 · How this solution was prepared and checked