Warm-Up 1
Math 1 Summer Bridge
Day 7: Exponential Relationships
Recognize growth or decay by repeated multiplication.
Student Goal
I can identify exponential relationships and interpret the starting value and growth factor.
Why It Matters
Exponential relationships describe situations like doubling, repeated percent change, savings growth, and decay.
Warm-Up
Warm-Up 2
In y = 5(2)^x, what is the starting value?
Short Lesson
Standard Focus
NC.M1.F-LE.1 and NC.M1.F-LE.2: Exponential functions
Student-Friendly Standard Goal
I can distinguish linear and exponential relationships and build simple exponential models.
- Exponential relationships multiply by the same factor each step.
- Linear relationships add the same amount each step.
- A simple exponential model has the form y = a(b)^x.
- a is the starting value and b is the growth or decay factor.
Guided Examples
Guided Example 1
Identify the Growth Factor
The table shows an exponential pattern. Find the growth factor.
Step 1
4, 12, 36, 108
What do you multiply by each step?
Guided Example 2
Compare Linear and Exponential
Which relationship is exponential?
Step 1
Table A: 2,5,8,11
What kind of pattern is Table A?
Practice
Problem 1
Which sequence has a common ratio of 4?
Problem 2
In y = 12(0.5)^x, the relationship shows...
Problem 3
For y = 3(2)^x, find y when x = 2.
Problem 4
Error analysis: A student says 5, 10, 15, 20 is exponential because it increases. What is wrong?
Problem 5
True or false: 1, 3, 9, 27 is exponential.
Reflection
How are you feeling about today's skill?
Optional reflection: What is one step, word, or representation from today that you want to remember when Math 1 starts?