Math 1 · Unit 7 · Lesson 3
Growth and Decay
The value of b decides the direction. Bigger than 1, each step makes the output bigger: growth. Between 0 and 1, each step keeps only a fraction: decay. Exactly 1 changes nothing, a flat line. Then percents: growing 10% means keeping 100% and adding 10%, a factor of 1.10; losing 25% means keeping 75%, a factor of 0.75. Convert both ways.
The big idea
The growth factor b lives next to 1, and 1 is the do-nothing number. A factor above 1 makes each step bigger, so the curve grows; a factor between 0 and 1 keeps only part of each step, so the curve decays; a factor of exactly 1 changes nothing and gives a flat line, which is why it is not counted as exponential. Stories give percents, and the factor is the percent measured from 100%: growing 10% means 110%, a factor of 1.10, and losing 25% means keeping 75%, a factor of 0.75. Going the other way, a factor above 1 minus 100% is the growth rate and 100% minus a factor below 1 is the decay rate. In a story, a is the amount at the start and b says what fraction remains or how much more there is each step.
The parts of this lesson
Each part is its own short page. Go in order, or pick the one you need.
Printables
One page with the three cases of b, the percent-to-factor rule both ways, story meanings of a and b, and worked conversions. Plus a worksheet with an answer key and a short lesson plan.