Math 1 · Unit 7 · Lesson 5 · part 3 of 6
Stories, clue words, and the race
Stories tell you which family with their words, if you listen for them.
Stories, clue words, and the race
Stories tell you which family with their words, if you listen for them.
Linear clue words
per, each, every with a fixed amount: $10 per month, 3 inches each week, 50 people every year. The same amount is added each step.
Exponential clue words
doubles, triples, halves, a percent each step: doubles every day, loses 20% a year, grows 5% a month. The same factor multiplies each step.
Watch the trap
"Grows by 10 each year" adds 10: linear. "Grows by 10% each year" multiplies by 1.10: exponential. One small word, a different family.
Here is the classic race. Town A has 145 people and gains 10 people a year: y = 145 + 10x, linear. Town B has 145 people and grows 10% a year: y = 145 · 1.10x, exponential. For the first few years Town A is barely behind or even ahead in the rounding, but the exponential town's yearly gain keeps growing (14, 16, 18, 19, 21 ...) while Town A's stays at 10. By year 8 Town B has 311 to Town A's 225, and the gap only widens.