Math 1 · Unit 8 · Lesson 5
When Money Shrinks, and Using the Models
The same form works when value goes down. A car that loses 13% a year keeps 1 minus 0.13, so its factor is 0.87. Always start from 1, keeping all of it: a factor of 0.85 means losing 15%, not 85%. Interest can work against you too, because debt grows the same way savings do. Then use the models: change the start or the rate and say what happens, and answer how-long questions with a table.
The big idea
Every factor in this unit is 1 plus or minus the rate, because keeping all of something is multiplying by 1. Growth adds to the 1, so 5% growth is 1.05. A loss takes away from the 1, so a car losing 13% a year has a decay factor of 0.87 and a value of P(1 minus r) to the t. Read the rate as the distance from 1: a factor of 0.85 means losing 15%, not 85%. Interest follows the same form whether it works for you in savings or against you on a debt. A model is for using: change the starting value and every output changes by the same factor; change the rate and the gap widens every year. How-long questions, like the doubling time, are answered with a table, and 72 divided by the rate is a quick check.
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 decay factor, the start-from-1 rule in both directions, the car example, debt, the what-if changes, and the doubling-time table with the 72 check. Plus a worksheet with an answer key and a short lesson plan.
Where this goes next
NC Math 1 standards in this lesson: NC.M1.F-IF.8b (interpret growth and decay rates), NC.M1.F-LE.5 (interpret the parameters in context), NC.M1.A-SSE.1a (interpret the parts of an expression), NC.M1.A-CED.1 (create equations to solve problems).