Math 1 · Unit 7 · Lesson 6
Building and Using Exponential Models
Build a model from a story, a table, or two points: a is the start and b is the factor. Then use it. Forward: given x, evaluate, power first. Backward: given y, use a table or draw the target as a horizontal line and find where the curve crosses it, the same crossing idea as a system in Unit 6. Say what a and b mean in the story, decide whether the situation is discrete or continuous, and ask what would change if a or b changed.
The big idea
An exponential model is y = a times b to the x with a and b read from the situation: a is the starting amount and b is the factor, built from a percent by starting at 100%. A story, a table, or two points with one at x = 0 all give a and b the same way. Forward questions put x in and evaluate, power first. Backward questions have no solving tool yet, so you use a table or draw the target value as a horizontal line and read where the curve crosses it, the same crossing idea that solved a system in Unit 6. Say what a and b mean in the story, decide whether the situation is discrete or continuous, and ask what the graph would do if a or b changed: that is the family-of-graphs question asked about the real world.
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 ways to build a model, forward and backward questions, the target-line picture, discrete versus continuous, and the what-changes habit. Plus a worksheet with an answer key and a short lesson plan.