Cogito
Integrated Math 1 · Chapter 4 · Lesson 2
Comparing Linear and Exponential
Which model does the data want?
12 problems · about 21 minutes · F-LE.A.1, F-LE.A.3
What this lesson teaches
The student decides between linear and exponential models from tables, graphs and context.
- Constant differences mean linear; constant ratios mean exponential.
- An exponential can look straight over a short range, so check the ratios.
- Any percentage change is exponential.
Warm Up
Straightforward practice. Get the method working first.
5 problems6, 12, 24, 48. Linear or exponential? 1 or 2.
Answer 2
Why Exponential.
What check distinguishes the two models in a table?
Answer Constant differences mean linear; constant ratios mean exponential.
Why Differences against ratios.
2, 6, 18, 54. Linear or exponential? 1 or 2.
Answer 2
Why Constant ratio of 3.
7, 12, 17, 22. Linear or exponential? 1 or 2.
Answer 1
Why Constant difference of 5.
2, 6, 18, 54. What is the common ratio?
Answer 3
Why 6 ÷ 2.
Build It Up
The same ideas with more to keep track of.
3 problems7, 12, 17, 22. What is the common difference?
Answer 5
Why 12 − 7.
100, 50, 25, 12.5. What is the common ratio?
Answer 0.5
Why 50 ÷ 100.
A savings account paying 4% a year. Linear or exponential? 1 or 2.
Answer 2
Why Percentage change.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsWhich signal identifies an exponential relationship?
Answer Equal ratios between consecutive outputs; A constant percentage change
Why Two of these describe a linear relationship.
3, 9, 27, 81. What is the common ratio?
Answer 3
Why 9 ÷ 3.
The Table: 5, 10, 20, 40. Is it linear or exponential? 1 linear, 2 exponential.
Answer 2
Why Exponential.
The Other Table: 4, 9, 14, 19. Linear or exponential? 1 or 2.
Answer 1
Why Linear.