Cogito
Algebra 1 · Chapter 6 · Lesson 1
Exponential Growth and Decay
Multiplying by the same factor, over and over.
10 problems · about 20 minutes · F-LE.A.1, F-LE.A.2, F-IF.C.8
What this lesson teaches
The student writes and interprets exponential functions modelling growth and decay.
- An exponential multiplies by the same factor each step.
- y = a · bˣ, with a the start and b the factor.
- b above 1 grows; b between 0 and 1 decays.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Systems in Context: x + y = 12 and x − y = 2. What is x?
Answer 7
Why 7.
Review — Solving Systems by Graphing: Slopes 3 and 3, intercepts 1 and 4. How many solutions?
Answer 0
Why None.
Warm Up
Straightforward practice. Get the method working first.
4 problemsy = 4 · 2ˣ. What is y when x = 3?
Answer 32
Why 32.
What distinguishes exponential from linear growth?
Answer A constant ratio between steps, not a constant difference.
Why A constant multiplier.
y = 2 · 3ˣ. What is y when x = 3?
Answer 54
Why 2 × 27.
y = 5 · 2ˣ. What is y when x = 0?
Answer 5
Why Anything to the power 0 is 1.
Build It Up
The same ideas with more to keep track of.
2 problemsA 20% fall each year. The decay factor as a percent?
Answer 80
Why 100 − 20.
Does an exponential add or multiply each step?
Answer Multiplies.
Why A line is the one that adds.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsDoubling: y = 3 · 2ˣ. What is y when x = 4?
Answer 48
Why 48.
The Factor: A quantity rises 6% each year. What is the growth factor, as a percent of the original?
Answer 106 percent
Why 106%, so b = 1.06.