# Linear Interpolation and Extrapolation

## Linear interpolation helps use the building blocks of geometry to solve algebraic unknowns. Work to identify the values between and beyond known points.

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Linear Interpolation and Extrapolation

### Interpolation & Extrapolation (for linear data)

1) We use linear interpolation to _______ in our data—that is, to estimate values that fall in between the values we already know.

2) For non-linear data, linear interpolation _________accurate enough for our purposes.

3) Polynomial interpolation works best for ________data.

4) Linear _________ can help us estimate values that are outside the range of our data set.

5) The fundamental goal of linear interpolation and extrapolation is to make an _______ even if you don't have an exact data point for confirmation.

Review: Interpolation Practice:

The Center for Disease Control collects information about the health of the American people and behaviors that might lead to bad health. The following table shows the percent of women who smoke during pregnancy.

Year Percent of pregnant women smokers
1990 18.4
1991 17.7
1992 16.9
1993 15.8
1994 14.6
1995 13.9
1996 13.6
2000 12.2
2002 11.4
2003 10.4
2004 10.2

Estimate the percentage of pregnant women that were smoking in the year 1998.

Review: Extrapolation Practice:

Winner Country Year Time (seconds)
Mary Lines UK 1922 12.8
Leni Schmidt Germany 1925 12.4
Gerturd Glasitsch Germany 1927 12.1
Tollien Schuurman Netherlands 1930 12.0
Helen Stephens USA 1935 11.8
Lulu Mae Hymes USA 1939 11.5
Fanny Blankers-Koen Netherlands 1943 11.5
Marjorie Jackson Australia 1952 11.4
Vera Krepkina Soviet Union 1958 11.3
Wyomia Tyus USA 1964 11.2
Barbara Ferrell USA 1968 11.1
Ellen Strophal East Germany 1972 11.0
Inge Helten West Germany 1976 11.0
Marlies Gohr East Germany 1982 10.9
Florence Griffith Joyner USA 1988 10.5

Use the data to estimate the winning time for the female 100-meter race in 1920. Use linear extrapolation because the first two or three data points have a different slope than the rest of the data.

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