Which formula correctly calculates the percent change in population between two consecutive years?

• A. [(pop_year2 − pop_year1) / pop_year1] × 100
• B. [(pop_year2 − pop_year1) / pop_year2] × 100
• C. (pop_year2 / pop_year1 − 1) × 100
• D. [(pop_year1 − pop_year2) / pop_year1] × 100

Answer: (B)

Percent change shows how much a quantity has grown or shrunk compared with the starting value. When you compare population from one year to the next, the natural base is the population in the initial year. So you take the difference (year2 minus year1) and divide by the starting population (year1), then multiply by 100 to get the percentage: (year2 − year1) / year1 × 100. This is algebraically the same as (year2 / year1 − 1) × 100, since dividing the difference by the initial year is the same as subtracting 1 after dividing year2 by year1.

The form that divides by the final year (year2) instead of the initial year measures change relative to the ending value, which is a different way to express proportional change. While it can be useful in some contexts, the conventional percent change between two consecutive years uses the initial year's population as the base.