Growth factor
SAT glossary · Math
Definition
The number b in y = a · b^x that you multiply by each time the input rises by one; b = 1+r with r the rate as a decimal (b>1 growth, 0<b<1 decay). The trap: the growth factor is what REMAINS, not what is lost — a 12% decrease gives b = 0.88, and the distractor uses 0.12, confusing "decreases by 12%" with "decreases to 12%."
Growth factor in plain English
In an exponential function y=a· b^x, the number b is called the growth factor, and it tells you exactly what to multiply by every time the input goes up by 1. It's connected to percentage rate r by the formula b=1+r — if b is bigger than 1, you're growing; if it's between 0 and 1, you're shrinking (decaying). Here's the trap: the growth factor represents what's LEFT after the change, not the amount that disappeared. So a 12% DECREASE means you keep 88% of what you had, giving b=0.88 — but a tempting wrong answer just uses the raw percentage itself, 0.12, mixing up 'decreases BY 12%' (you lose 12%, keep 88%) with 'decreases TO 12%' (you'd have almost nothing left).
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