1. Lesson 3.6 Nonlinear Models
Essential Question: How do you fit nonlinear models to data?

2. Classifying Scatter Plots
A scatter plot can be used to give you an idea of which type of model will best fit a set of data.

3. What type of model should you use for the following data. 2, 1 , 2

4. What type of model should you use for the following data. 2, 2 , 2

5. What type of model should you use for the following data. 2, 1. 9 , 2

6. Fitting Nonlinear Models to Data
Once you have used a scatter plot to determine the type of model that would best fit a set of data, there are several ways that you can actually find the model. Each method is best used with a computer or calculator, rather than with hand calculations.

7. How do you fit nonlinear models to data?
Use a scatter plot to decide which models might fit the data.
Use the regression feature to fit each model to the data.
Check how closely the model fits the data.

8. The table shows the kinetic energy of a ball at different speeds
The table shows the kinetic energy of a ball at different speeds. Find the model that best fits the data. Make a scatter plot of the data. Find quadratic, exponential, and power models.
Speed (m/s)
Kinetic Energy (N)
0.9
0.016
1.0
0.019
1.5
0.040
1.8
0.061
2.1
0.087
2.2
0.092
2.4
0.111

9. Fit an exponential model to the data in the table
Fit an exponential model to the data in the table. Use your model to estimate the amount remaining after 17.5 years.
Time (years)
Mass of Tritium (g)
2.5
0.373
3.2
0.358
5.7
0.310
8.1
0.275
11.6
0.226
14.2
0.193
15.8
0.179

10. The number of snails y in a tidepool after x weeks is given in the table. Fit a logistic model to the data. Estimate when there were 10 snails. x y 3 4 7 9 11 12 18 16 26 19 29 21 31 25 33 27

11. The table below shows the amounts of revenue R (in billions of dollars) collected by the Internal Revenue Service (IRS) for selected years from 1963 through Use a graphing utility to find a model for the data. Then use the model to estimate the revenue collected in (Source: IRS Data Book)
Year
Revenue, R
1963
105.9
1968
153.6
1973
237.8
1978
399.8
1983
627.2
1988
935.1
1993
1176.7
1998
1769.4
2003
1952.9
2008
2745.0

12. To estimate the amount of defoliation caused by the gypsy moth during a given year, a forester counts the number x of egg masses on 1 40 of an acre (circle of radius of 18.6 feet) in the fall. The percent of defoliation y the next spring is shown in the table. Use the regression feature of a graphing utility to find a logistic model for the data. How closely does the model represent the data?
Egg Masses, x
Percent of defoliation, y 12 25 44 50 81 75 96
100 99

13. How do you fit nonlinear models to data?

14. Ticket Out the Door
What type of model should you use for the following data?
(2, 28.0), (3, 25.6), (7, 20.6), (8, 19.9), (10, 18.5), (13, 17.0), (14, 16.8), (17, 15.7)