1.3. Models and Data http://www.ck12.org
This example suggests that the sine over timetis a function that is used in a variety of modeling situations.
Caution:Although the fit to the data appears quite good, do we really expect the number of trips to continue to go
up and down in the future? Probably not. Here is what the graph looks like when projected an additional ten years:
Exponential Models
Our last class of models involves exponential functions. Exponential models can be used to model growth and decay
situations. Consider the following data about the declining number of farms for the years 1980 - 2005.
Example 4:
The number of dairy farms has been declining over the past 20+years. The following table charts the decline:
TABLE1.4:
Year Farms (thousands)
1980 334
1985 269
1990 193
1995 140
2000 105
2005 67We enter the data in our calculator in L5 (entering the year 1980 as 1, the year 1985 as 2, etc.) and L6. We then will
view a scatter plot. Change the window ranges accordingly to include all of the data. For the largey−values, choose
the range[− 50 , 350 ]with a scale of 25.
Here is the scatter plot:
Now let us compute the regression equation. Since our scatter plot suggests an exponential model for the data, we
will chooseExponential Regressionfrom the menu. We get the equation:y= 490. 6317 ∗. 7266 x
Let’s graph the equation over our data. We see the following graph:
In the homework we will practice using our calculator extensively to model data.