This examplesuggeststhat the sine over time is a functionthat is usedin a varietyof modelingsituations.
Caution:Althoughthe fit to the data appearsquitegood,do we reallyexpectthe numberof trips to continue
to go up and downin the future?Probablynot. Hereis what the graphlookslike whenprojectedan additional
ten years:
ExponentialModels
Our last classof modelsinvolvesexponentialfunctions.Exponentialmodelscan be usedto modelgrowth
and decaysituations.Considerthe followingdataaboutthe decliningnumberof farmsfor the years
1980–2005.
Example4:
The numberof dairyfarmshas beendecliningover the past 20+ years.The followingtablechartsthe decline:
Year Farms(thousands)
1980 334
1985 269
1990 193
1995 140
2000 105
2005 67We enterthe data in our calculatorinL5(againenteringthe yearsas 1, 2, 3...) andL6. We then will view
a scatterplot. Changethe windowrangesaccordinglyto includeall of the data.For the large -values,
choosethe range with a scaleof
Hereis the scatterplot:
Now let us computethe regressionequation.Sinceour scatterplot suggestsan exponentialmodelfor the
data,we will chooseExponentialRegressionfrom the menu.We get the equation: