CK-12-Calculus

http://www.ck12.org Chapter 1. Functions, Limits, and Continuity

Let’s graph the equation over our data. We see the following graph:

Trigonometric Models
The following example shows how a trigonometric function can be used to model data.
Example 3:
With the skyrocketing cost of gasoline, more people have looked to mass transit as an option for getting around. The
following table uses data from theAmerican Public Transportation Associationto show the number of mass transit
trips (in billions) between 1992 and 2000.

TABLE1.3:

year Trips (billions)

1992 8. 5

1993 8. 2

1994 7. 93

1995 7. 8

1996 7. 87

1997 8. 23

1998 8. 6

1999 9. 08

2000 9. 4

We enter the data in our calculator inL5andL6, starting in L5 with the number one for 1992 (the first year). We
then will view a scatter plot. Change the window ranges accordingly to include all of the data. Use[− 2 , 10 ]for both
xandyranges.
Here is the scatter plot:

Now let us compute the regression equation. Since our scatter plot suggests a sine model for the data, we will choose
Sine Regressionfrom the menu. We get the equation:

y=. 9327 ∗sin(. 4681 x+ 2. 8734 )+ 8. 7358.

Let us graph the equation over our data. We see the following graph: