Cogito
Algebra 1 · Chapter 6 · Lesson 3
Comparing Linear and Exponential Growth
Adding the same, or multiplying by the same.
11 problems · about 23 minutes · F-LE.A.1, F-LE.A.3
What this lesson teaches
The student distinguishes linear from exponential growth and recognises that exponential eventually wins.
- Linear growth has a constant difference; exponential growth has a constant ratio.
- Test differences first, then ratios.
- Any exponential growth eventually overtakes any linear growth.
Warm Up
Straightforward practice. Get the method working first.
4 problems3, 12, 48. Common ratio?
Answer 4
Why 4.
4, 8, 12, 16. Common difference?
Answer 4
Why Constant addition.
4, 8, 16, 32. Common ratio?
Answer 2
Why Constant multiplication.
100, 50, 25. Common ratio, as a decimal?
Answer 0.5
Why Halving.
Build It Up
The same ideas with more to keep track of.
3 problemsDoes exponential growth eventually overtake linear? 1 for yes, 0 for no.
Answer 1
Why Given enough steps.
Sort each sequence by its kind of growth.
Answer Linear: 2, 5, 8, 11, 10, 20, 30, 40 · Exponential: 2, 4, 8, 16, 1, 3, 9, 27
Why Take differences first, then ratios.
Start 5, double each step. Value after 3 steps?
Answer 40
Why 5 × 2 × 2 × 2.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsStart 5, add 3 each step. Value after 3 steps?
Answer 14
Why 5 + 9.
Is a constant ratio the sign of linear or exponential? 1 for linear, 2 for exponential.
Answer 2
Why Ratios go with multiplying.
The Difference: 5, 9, 13, 17. What is the common difference?
Answer 4
Why 4.
The Ratio: 2, 6, 18, 54. What is the common ratio?
Answer 3
Why 3.