1. Fitting Curves to Data
Lesson 4.4B

2. Using the Data Matrix Consider the table of data below.
It is the number of Widgets sold per year by Snidly Fizbane's Widget Works (with 1990) being year zero.
Place these numbers in the data matrix of your calculator.
Plot the points.
We seek the function which models this data.
This will enable Snidly to project sales for the immediate future and set budgets
What type of function does it appear to be?
Year
Number of Widgets
150 1
175 2
207 3
235 4
260 5
300 6
370

3. What Kind of Function? It might be linear
But it appears to have somewhat of a curve to it
Check the successive slopes – place cursor at top of column c3
Enter expression

4. What Kind of Function? The slopes are not the same
It is not linear
We will check to see if it is exponential
In column 4 have the calculator determine 1.*ln(c2)
The text calls this “transforming” the data
Enabling us to determine if we have an exponential function

5. What Kind of Function? Now see if the ln values are equally spaced
If graphed would they be linear?
Use the c4 – shift(c4) function in column 5
You should find that they are not exactly equal but they are quite close to each other

6. Plotting the New Data Specify columns to be plotted
x values from column 1
y values from column 4 (these are the ln(c2) values)
This should appear to be much closer to a straight line

7. Plotting the New Data
Now use the linear regression feature of your calculator
Determine the equation of the line for these points
x values come from column 1, y values from column 4

8. Figuring the Original Equation
Column 2 had w the number of widgets
We took ln(w) to get the y values we plotted
That means we have
Now we need to solve the equation to solve the above equation for w
Hint … raise e to both sides of the equation

9. Figuring the Original Equation
Solving for w
Now we end up with an exponential function
Now graph the original points (x, widgets)

10. Figuring the Original Equation
The results would be something like this
Actually, our calculator could have taken the original points and used exponential regression

11. Exponential Regression
Note the option on the regression menu
Check for accuracy

12. Summary of Steps
List the ordered pairs in adjacent columns of the data matrix
In a third column have the calculator place   ln(  )  of the y values
Plot (x, ln(y)) and note that it is a line
Use linear regression with the x column and the ln(y) column. The text may suggest draw a line by eye and determine the equation manually
This gives us  ln(y) = m*x + b
Solve the above function for y
It will be in the form y = A * eB*x
This is the exponential function which models the original set of points (x, y)

13. Assignment
Lesson 4.4B
Page 183
Exercises 18 – 21 all