Math 1 · Unit 7 · Lesson 2
The Form y = a · bx
Ask the three family questions. What family? The exponential family, y = a times b to the x. What are its numbers? a and b. What does each do? a is the starting value and the y-intercept, because b to the zero is 1 and a times 1 is a. b is the growth factor, what you multiply by each step. Build a table from the equation, plot the curve, and move a and b in the explorer.
The big idea
The exponential family has one form, y = a times b to the x, and two numbers with two jobs, exactly the way lines had y = mx + b with m and b. The number a is the starting value and the y-intercept, and the reason is the secret multiply-by-1 from Unit 1: at x = 0 the power b to the zero is 1, so y is a times 1, which is a. The number b is the growth factor, the constant ratio you multiply by for each step to the right. Build a table by starting at a and multiplying by b; evaluate with function notation by doing the power first and then multiplying by a. In the explorer, a moves where the curve starts and b changes how fast it multiplies, the way b slid a line and m tilted it.
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 questions, the two jobs and the multiply-by-1 reason, table building, power-first evaluation, and a worked example. Plus a worksheet with an answer key and a short lesson plan.