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Exponential Growth. According to legend, chess was invented by Grand Vizier Sissa Ben Dahir, and given to King Shirham of India. The king offered him a reward, and he requested the following: .
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Exponential Growth According to legend, chess was invented by Grand Vizier Sissa Ben Dahir, and given to King Shirham of India. The king offered him a reward, and he requested the following: • "Just one grain of wheat on the first square of the chessboard. Then put two on the second square, four on the next, then eight, and continue, doubling the number of grains on each successive square, until every square on the chessboard is reached."
Exponential Growth You may give me the wheat or its equal value on the 64th day. This is all I require for my services. The king agreed, but he lost his entire kingdom to Sissa Ben Dahir. Why? Sources: http://muller.lbl.gov/teaching/Physics10/physics%2010%20notes/DoublingRule.html http://www.blarg.net/~math/y2l2p.html http://members.nbci.com/Templarser/chess.html
Exponential Growth square/day rice Sum 1 1 1 2 2 3 3 4 7 4 8 15 5 16 31 6 32 63 7 64 127 ... 64 _____ _____ How much wheat did the King owe for 64th day? How much wheat in all?
Exponential Growth In all, the king owed about 18,000,000,000,000,000,000 grains of wheat. This was more than the worth of his entire kingdom!
Exponential Growth There is a function related to this story: f(x)=2^x day rice sum rice day rice 2^(day-1) 2^day-1 1 1 2^0 = ____ 2^1 - 1 = ____ 2 2 2^1 = ____ 2^2 - 1 = ____ 3 4 2^2 = ____ 2^3 - 1 = ____ 4 8 2^3 = ____ 2^4 - 1 = ____ ... 64 ____ 2^63 = ____ 2^64-1 = ____ Copy and fill out this chart.
Exponential Growth Moore's Law (from the intel website): http://www.intel.com/research/silicon/mooreslaw.htm
Exponential Growth Gordon Moore (co-founded Intel in 1968) made his famous observation in 1965, just four years after the first planar integrated circuit was discovered. The press called it "Moore's Law" and the name has stuck. In his original paper, Moore predicted that the number of transistors per integrated circuit would double every 18 months. He forecast that this trend would continue through 1975. Through Intel's technology, Moore's Law has been maintained for far longer, and still holds true as we enter the new century. The mission of Intel's technology development team is to continue to break down barriers to Moore's Law.
Exponential Growth chip Year Transistors 4004 1971 2,250 8008 1972 2,500 8080 1974 5,000 8086 1978 29,000 286 1982 120,000 386 processor 1985 275,000 486 DX processor 1989 1,180,000 Pentium® processor 1993 3,100,000 Pentium II processor 1997 7,500,000 Pentium III processor 1999 24,000,000 Pentium 4 processor 2000 42,000,000 Produce a plot of year vs. transistors
Exponential Growth- Moore’s Law chip Year Transistors 4004 1971 2,250 8008 1972 2,500 8080 1974 5,000 8086 1978 29,000 286 1982 120,000 386 processor 1985 275,000 486 DX processor 1989 1,180,000 Pentium® processor 1993 3,100,000 Pentium II processor 1997 7,500,000 Pentium III processor 1999 24,000,000 Pentium 4 processor 2000 42,000,000 Produce a plot of year vs. transistors (from the intel website): http://www.intel.com/research/silicon/mooreslaw.htm
Exponential Growth Review of how to do a point plot: "STAT" "Edit" enter year in L1 and transistors in L2. "2nd" "Y=" "Plotsoff" "Enter" “Enter" "2nd" "Y=" Choose Plot1 {On, Scatterplot, L1, L2, mark} "Zoom" 9
Exponential Growth 1. Describe the graph: 2. How does this relate to the rice problem? 3. Can you think of other things that “grow” this way (ie. Doubling over a constant period of time?)
