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# chapter 1 15 - 18 19 20 SECTION12 MATHEMATICALMODELS El 15...

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Unformatted text preview: 18. ( 19. 20. SECTION12 MATHEMATICALMODELS El 15 230 (chirps/min) 5 - 95 (°F) 45 0 Using a computing device, we obtain the least squares 3) (b) 270 (chirps/min) 105 (°F) 4 E regression line y : 4.8509: — 220.90. (c) When w 2 100° F, y = 264.7 m 265 chirps/min. (a) 20 (ﬂ) (b) 20 (a) 0I 189610 2000 (year) 18961 2000 (year) A linear model does seem appropriate. Using a computing device, we obtain the least squares regression line y : 00891197471 — 1582403249, where cc is the year and y is the height in feet. (c) When :5 = 2000, the model gives y N 20.00 ft. Note that the actual winning height for the 2000 Olympics is less than the winning height for 1996—so much for that prediction. (d) When :1: = 2100, y N 28.91 ft. This would be an increase of 9.49 ft from 1996 to 2100. Even though there was an increase of 8.59 ft from 1900 to 1996, it is unlikely that a similar increase will occur over the next 100 years. By looking at the scatter plot of the data, we rule out 610 C0510" 3;) the linear and logarithmic models. 45 100 (Reduction %) 0. Scatter plot We try various models: Quadratic: y = 0.4902:2 — 62.28%:c + 1970.630 Cubic: y = 0.0201243201cc3 — 3.88037296cm + 24767544683: — 5163935198 Quartic: y = 0000295104924 — 00654560995903 + 527525641132 — 18022665112 + 2203210956 Exponential: y = 241422994 (1.054516914)m Power: y = 0.000022854971323-616078251 ...
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