Math 1 · Unit 7 · Lesson 2 · part 2 of 6
Three questions for a new family
Every new family gets the same three questions (Unit 3, Lesson 3).
Three questions for a new family
Every new family gets the same three questions (Unit 3, Lesson 3). Here they are for the exponential family.
- 1What family is this?The exponential family. Its form is y = a · bx: a number a, times a base b raised to the x. Lines were y = mx + b; this is the next family.
- 2What are its numbers?The parameters a and b. Give me an a and a b and you have named one member of the family.
- 3What does each number do?a is the starting value, the output when x = 0, and the y-intercept. b is the growth factor, the number you multiply by each step.
Why a is the y-intercept: the secret multiply-by-1Put x = 0 into y = a · bx. Lesson 1 showed that b0 = 1. So y = a · 1 = a. Multiplying by 1 is doing nothing (Unit 1, Lesson 1), so at x = 0 the function is exactly where it started. That is why a is the starting value and where the curve crosses the y-axis, the same way b in y = mx + b was the y-intercept because the mx part became 0.
y = a · bx a: start here. b: multiply by this each step.