1. Comparing Exponential and Linear Functions
Lesson 3.2

2. Table of Values
Use the data matrix of your calculator to enter the following values.
Column 1 is the x values
Columns 2 and 3 are the f(x) and g(x) x 1 2 3 4 5 6 7
f(x) 12 18 24 30 36 42 48 54
g(x)
15.6
20.3
26.4
34.3
44.6
57.9
75.3

3. Table of Values
Click APPS then 6, then Current (F1, 8 to clear if needed)
Enter values as shown below

4. Two Different Functions
Note the succession of values for f(x)
Differ by 6 each
This implies linear

5. Two Different Functions
Note the succession of values for g(x)
They do NOT differ by a constant
However, the successive values have the same ratio
Show by placing formula in column 4
This shows it is an exponential function.
Cursor must be here
Note ratio is 1.3

6. How to Determine the Formula
From previous lesson we know that
Where b is the growth factor
In our case the common ratio = 1.3
Solve for a
Substitute b = 1.3, any ordered pair

7. Determine Function from Two Points
We can create two equations with two unknowns
Solve for one of the variables
Substitute into the other equation •
(-1, 2.5)
(1, 1.6) •
Answer
b=0.8 a=2

8. Compare and Contrast Linear y = m*x + b y = m+m+ … m+ b x terms
Exponential y = a * bx y = a * b * b * … * b x factors

9. Compare and Contrast
Exponential growth will always outpace linear growth
In the long run
Eventually
Question: Where?
Solve graphically or algebraically or observe table

10. Where Exponential Passes Linear
Given y = 100 (1.02)x y = x
Algebraically : no current tools to solve (1.02)x = x
Graphically : ask calculator to find intersection
Or observe tables

11. Assignment
Lesson 3.2
Page 119
Exercises 1 – 41 odd