1. 6-7 Modeling with Exponential Functions

2. Recognizing Different Types of Models
Linear with a positive slope
Quadratic
Logarithmic
Linear with a negative slope
Exponential

3. Gaussian Model Exploring Logistic and Gaussian models
Domain: All Real Numbers
Range: (0,1]
No x-intercepts; graph approaches but never reaches y=0
y-intercept: (0,1)
Asymptotes: x-axis

4. Logistic Model Domain: All Real Numbers Range: (0,1) No x-intercepts
y-intercept: (0, 0.5)
Asymptote: x-axis, y=1

5. Classifying Data Sets Quadratic Function Exponential Function x -2 2 42 4 6 8 10 y 32 72
128
200 X -2 -1 1 2 3 4 Y 9 27 81
241
First Differences -8 8 24 40 56 72
Second Differences 16 16 16 16 16

6. Writing an Exponential Function using Two Points
First: Set up system of two equations with two variables
From the first equation, find a
Plug in a into second equation
Take only the positive square root because b is positive in exponential functions

7. Finding an Exponential Model
A store sells trampolines. The table shows the number of trampolines, y, sold during the xth year that the store has been open. Write a function that models the data.
Make a scatter plot of the data x y 1 12 2 16 3 25 4 36 5 50 6 67 7 96
The data appears exponential

8. Create two equations using two points like (1,12) and (4,36)
From the previous slide x y 1 12 2 16 3 25 4 36 5 50 6 67 7 96
Create two equations using two points like (1,12) and (4,36)
Substitute into the second equation