Percent Change and the Growth Factor

A 5 percent raise means your new amount is the old amount plus 5 percent more of it: 100 percent plus 5 percent, or 105 percent of the original. Written as a decimal multiplier, that's 1.05. So instead of tracking the original amount and the increase separately, you fold them into one number and multiply once. That single number, 1.05, is the growth factor. The same logic runs in reverse for a decrease: losing 12 percent leaves you with 100 percent minus 12 percent, or 88 percent of the original, so you multiply by 0.88. The growth factor is always 1 plus the percent change as a decimal, using a negative rate for a decrease.

This matters most when a change repeats. Each time period, you apply the growth factor to whatever amount exists at that point, not to the original amount. That's why three straight years of 10 percent growth beats a flat 30 percent increase: year two's 10 percent grows an amount that already includes year one's growth, and year three grows an amount that includes both earlier increases. Multiplying 1.10 by itself three times gives 1.331, not 1.30. Percent changes multiply across time; they don't add.

This connects directly to the rest of data analysis work: ratios describe a single comparison, growth factors describe how that comparison repeats over steps, and both feed into reading scatterplot models where growth or decay patterns show up as curves rather than straight lines.