Math 1 · Unit 7 · Lesson 3 · part 2 of 5
What b decides, and why
The value of b decides which way the curve goes, and the reason is one sentence from Unit 1: multiplying...
What b decides, and why
The value of b decides which way the curve goes, and the reason is one sentence from Unit 1: multiplying by a number bigger than 1 makes things bigger, multiplying by a number smaller than 1 makes things smaller, and multiplying by exactly 1 changes nothing.
b bigger than 1: growthEach step multiplies the output by more than 1, so it gets bigger. The graph rises from left to right, faster and faster. y = 100 · 1.5x: 100, 150, 225, 337.5.
b between 0 and 1: decayEach step keeps only a fraction of what was there, so the output gets smaller. The graph falls from left to right, flattening out. y = 100 · 0.5x: 100, 50, 25, 12.5.
b exactly 1: not really exponentialMultiplying by 1 changes nothing (the do-nothing number). y = 100 · 1x is just y = 100, a flat line.
In the explorer below you can slide b past 1 yourself and watch the switch. One more rule: b must be positive. A negative b would flip the sign back and forth every step (positive, negative, positive), which is not a smooth curve at all, so exponential functions always have b greater than 0.