Presentation on theme: "Tu/W 9/4,5 Honors Physics. A hypothesis can be used to predict the results of observations or the existence of other phenomena. There are two types of."— Presentation transcript:
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
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
A young man's parents kept track of his height through the years, as shown in this graph. DANGER OF EXTRAPOLATION
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
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
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
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
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?
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.
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.
PRECISE: R 2 ~ 1.00 NOT ACCURATE: SLOPE IS NOT PI
NOT PRECISE: R 2 IS NOT ~1.00 ACCURACY: SLOPE ~ PI
NOT PRECISE: R 2 IS NOT ~1.00 NOT ACCURATE: SLOPE IS NOT ~ PI
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: