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Tu/W 9/4,5 Honors Physics

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A hypothesis can be used to predict the results of observations or the existence of other phenomena. There are two types of predictions that can be made. One is called extrapolation; the other is called interpolation. INTERPOLATION AND EXTRAPOLATION

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Extrapolated predictions are those that are made outside of the known data points. MEMORY TIP: “exit” = how to get outside; “extrapolate” = predicted outside the data points Trends in the known data can often be used to make accurate extrapolated predictions; however, this is not always the case. EXTRAPOLATION

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A young man's parents kept track of his height through the years, as shown in this graph. DANGER OF EXTRAPOLATION

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Extrapolation shows that Bryan will be about 10 feet tall when he's 30 years old. What faulty assumption was made in this extrapolation? DANGER OF EXTRAPOLATION

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Interpolated predictions are those that are made between known data points. MEMORY TIP: “inter”state highways go between states; “inter”polations predict between data points INTERPOLATION

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An interpolation of this data would lead one to the prediction that Bryan was about 4.5 ft tall at the age of 14. Is this a reasonable prediction? INTERPOLATION

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Thanks to the genetic influence of my mother’s brothers (who range from 6’2” to 6’7”), my oldest child is 6’4”. Here’s his height data through the years: PREDICTING USING BEST-FIT LINES/CURVES AND THEIR EQUATIONS

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Note that the equation of the best-fit line for this data is given by y = 2.593x + 31.144 Translating this into something meaningful for height and age gives Height, in = (2.593 in/yr)(Age,yrs) + 31.144 in This means that if you need to find out the height when he was 5 years 3 months old, you’d calculate Height, in = (2.593inches/year)(5.25 yrs) + 31.144 in = 44.75725 inches. Does this seem reasonable? Why/why not?

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How old was this child when he was 5’0” tall? First, remember that the basic relationship is Height, in = (2.593 in/yr)(Age,yrs) + 31.144 in Let’s translate this into H for height in inches and A for age in years: H = 2.593A + 31.144 BUT Remember that you’re asked to find the Age at a certain Height, NOT the Height at a certain Age! To do this, it’s time for ALGEBRA.

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ALGEBRA TIME!!

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FINISHING UP

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IS IT ACCURATE? IS IT PRECISE? You can use information from your graph to determine the accuracy and precision of your data. Remember... Accuracy is how close the experimental data is to the accepted value; Precision is how close your points are to each other; in this case, how close all the points are to being on that best-fit line.

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PRECISE: R 2 ~ 1.00 ACCURATE: SLOPE ~ PI

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PRECISE: R 2 ~ 1.00 NOT ACCURATE: SLOPE IS NOT PI

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NOT PRECISE: R 2 IS NOT ~1.00 ACCURACY: SLOPE ~ PI

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NOT PRECISE: R 2 IS NOT ~1.00 NOT ACCURATE: SLOPE IS NOT ~ PI

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1.Make sure you have all questions answered and your graph/data printed BEFORE you come to class next time. 2.Download the Scientific Notation worksheet and complete it on your own paper. 3.Practice Scientific Notation questions online. Be ready for a quiz next class period! FOR NEXT TIME:

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