1. Which graph best describes your excitement for …..

3. We are going to analyze graphs and tables to make an informed decision as to which function would best model a given set of data.

4. Decision Making Exponential Quadratic The three most common are….
When given a data set and asked to find a model, it helps to first know what model is best.
The three most common are….
Linear
Exponential
Quadratic

5. Linear Models
Linear Models have a common ratio. When looking at a table, the change in y over the change in x should be the same. x y -3 7 -1 13 1 19 3 25 5 31 +6 +2 +6 +2 +2 +6 +2 +6

6. Exponential Models x y -2 -1 -8 -32 1 -128 2 -512
Exponential models have a common ratio. When looking at a table, the y values should appear to be multiplied by the same value. x y -2 -1 -8
-32 1
-128 2
-512
X 4 +1
X 4 +1 +1
X 4 +1
X 4

7. Quadratic Models
For quadratic data, the second differences are the same. If data have a common second difference, then you can model them with a quadratic function. x y -1 16 2 1 -2 4 3 20 +1
-14
-10 +1 -4
-10 +1 +6
-10 +1
+16

8. Graphing Calculator
It is often easiest to determine the best model by the shape of the graph. Then find the regression.
To do this:
1. Turn the scatter plot on using
2. Enter the data into : Edit
Press : Stat.
Analyze the shape of the graph.
Use CALC and choose LinReg, QuadREg or ExpReg.
2nd
Y =
STAT
ZOOM
STAT

9. Let’s Try Some!!!! x y -1 20 8 1
3.2 2
1.28 3
0.512

10. x y 1
1.5 2 6 3
13.5 4 24

11. The table below shows the population of a small town
The table below shows the population of a small town. Let t = 0 correspond to the year 1990.
a. Graph the data. Does the graph suggest a
linear, exponential, or quadratic model?
b. What is the difference in years?
c. Find the differences of consecutive terms.
Divide by the difference in years to find
possible common differences.
d. Write a linear equation to model the data
based on your answer to part (c).
e. Predict the population in 2020.
Year y
5100 5
5700 10
6300 15
6900 20
7500