## Exponential RegressionRecursive Formulas for a Sequence

To Clear All Lists: [2nd] [+] 4: ClearAllLists

Window settings: [ZOOM], 6:Standard

Make sure you use the [ (-) ] key for the values that are negative.

## Exponential Regression:

This is the data we for the quadratic regression.

 L1 L2 -3 11 -2 5 -1 2 0 0 1 2 2 5 3 11

This is the data for the exponential regression.

 L1 L2 0 6000 1 7500 2 9400 3 11300 4 13700 5 17300 6 20900

[STAT] - select EDIT    1: Edit

Enter Data into you calculator:

[STAT] - select CALC   5: QuadReg

[ 2nd ] [1] [ , ] [ 2nd ] [2] [ , ]

[VARS]     Y-Vars     1: Function

FUNCTION    1: Y1

[ENTER]

[ENTER]

[ Y= ]

[GRAPH]

Check to see if the points from the table fit the quadratic regression. First change the settings to plot a scatterplot graph of the data in the original table.

[ 2nd ] [Y = ]

[ENTER ]

[GRAPH]

[STAT] - select EDIT    1: Edit

Enter Data into you calculator:

[STAT] - select CALC   0: ExpReg

[ 2nd ] [1] [ , ] [ 2nd ] [2] [ , ]

[VARS]     Y-Vars     1: Function

FUNCTION    1: Y1

[ENTER]

[ENTER]

• note: to get r2 and r [2nd] [0] DiagnosticOn [ENTER]

[ Y= ]

[GRAPH]

Not Available at this time.

Check to see if the points from the table fit the exponential regression. First change the settings to plot a scatterplot graph of the data in the original table.

[ 2nd ] [Y = ]

[ENTER ]

[GRAPH]

Not Available at this time.

[ENTER]

## Alternative is to place the regression in Y1 after the regression is made.

Following:

[ENTER]

Place the regression data into Y1:

[ Y = ] [ VARS ] 5: Statistics

EQ 1: RegEQ

Another copy: TI-83+ Instructions

## Exponential RegressionRecursive Formulas for a Sequence

recursive formula: a formula used to define terms of a sequence by relating them to previous terms of the sequence

For example, tn = tn-1 + n, where t1 = 5, is a recursive formula.

A recursive formula that generates a sequence is dependent on one or more previous terms. It is not defined explicitly in terms of n. Since it is dependent on at least one previous term, at least one of the values of the terms must be stated. If tn is the nth term, then the previous term is tn-1.

 Example 1: Arithmetic Sequence List the first 7 terms for the a sequence with the recursive formula where t1 = 1, Create a table of values and graph the sequence. Solution Terms: 1, 5/2, 4, 11/2, 7, 17/3, 10 Because you are working with sequences, set your calculator to Seq mode and Dot mode (as shown). To generate the table of values for a sequence or to graph the sequence, you need to enter the function, which is the general term or explicit formula. To enter the function , where t1 = 1, press the following keystrokes: Since t1 = 1, enter the minimum value for u(nMin) as 1. Press the following keystrokes: Press to see the points of the sequence plotted. If there is no graph, you will have to adjust the window settings (domain and range). You may want to check the table of values to determine a suitable domain and range. To do this, press [ TABLE ]. Example 2: Geometric Sequence List the first 7 terms for the a sequence with the recursive formulawhere t1 = 1, Create a table of values and graph the sequence. Compare the sequences given in Example 1 and Example 2. Solution Terms: 1, 3/2, 9/4, 27/8, 7, 81/16, 243/64 Let , where t1 = 1, be the function represented by v(n). Press , select “v(n),” and enter the following: Now, you can display the table by pressing [ TABLE ] or you can display the graph of both sequences by pressing . To compare and contrast, you may want to change the window settings. PhotoDisc Collection/Getty Images

Parts of this work has been adapted from a Math 30 Pure learning resource originally produced and owned by Alberta Education

Comments to:  Jim Reed - Homepage