Calc08_2 - 8.2 Relative Rates of Growth Greg Kelly Hanford...

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8.2 Relative Rates of Growth Greg Kelly, Hanford High School, Richland, Washington
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The function grows very fast. x y e = We could graph it on the chalkboard: If x is 3 inches, y is about 20 inches: ( 29 3,20 At 10 inches, 1 mile 3 x y = = At 44 inches, 2 million light-years x y = = We have gone less than We have gone less than half-way across the board half-way across the board horizontally, and already the horizontally, and already the y-value would reach the y-value would reach the Andromeda Galaxy! Andromeda Galaxy! At 64 inches, the y-value At 64 inches, the y-value would be at the edge of the would be at the edge of the known universe! known universe! (13 billion light-years) (13 billion light-years)
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The function grows very slowly. ln y x = If we graph it on the chalkboard it looks like this: We would have to move 2.6 miles to the right before the line moves a foot above the x-axis! 64 inches By the time we reach the By the time we reach the edge of the universe again edge of the universe again (13 billion light-years) the
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