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# feb11 - MIT OpenCourseWare http/ocw.mit.edu 6.055J 2.038J...

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MIT OpenCourseWare http://ocw.mit.edu 6.055J / 2.038J The Art of Approximation in Science and Engineering Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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imports cars N 3 × 10 8 miles/year 10 4 gallons/mile 1 / 25 barrels/gallon 1 / 40 other uses 2 fraction imported 0.5 and it seems as if even babies own cars. As a guess, then, the number of cars is N 3 × 10 8 . The annual miles per car is maybe 15,000. But the N is maybe a bit large, so let’s lower the annual miles estimate to 10,000, which has the additional merit of being easier to handle. A typical mileage would be 25 miles per gallon. Then comes the tricky part: How large is a barrel? One method to estimate it is that a barrel costs about \$100, and a gallon of gasoline costs about \$2.50, so a barrel is roughly 40 gallons. The tree with numbers is: 2 Assorted subproblems 11 imports cars N miles/year gallons/mile barrels/gallon other uses fraction imported Now guess values for the unnumbered leaves. There are 3 × 10 8 people in the United States, All the leaves have values, so I can propagate upward to the root. The main operation is multiplication. For the ‘cars’ node: 10 4 miles 1 gallon 1 barrel 3 × 10 8 cars × 1 car–year × 25 miles × 40 gallons 3 × 10 9 barrels/year . The two adjustment leaves contribute a factor of 2 × 0 . 5 = 1 , so the import estimate is 3 × 10 9 barrels/year .
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