Exponential growth
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Transcript of Exponential growth
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Exponential growth
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.
Skills: noneConcepts: linear growth, exponential growth, linear scale plot, logarithmic scale plot, “hockey stick,” Moore’s Law, hosting in the cloud
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Where does this topic fit?
• Internet concepts– Applications– Technology– Implications
• Internet skills– Application development– Content creation– User skills
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Grow by the same amount in each time period
Grow by the same percent in each time period
Linear versus exponential growth
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Year
Growth 1 2 3 4 5 6 7 8 9 10
10% 10 11 12 13 15 16 18 19 21 24
20% 10 12 14 17 21 25 30 36 43 52
50% 10 15 23 34 51 76 114 171 256 384
100% 10 20 40 80 160 320 640 1280 2560 5120
Exponential growth
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Exponential growth, linear scale
Twelve year, 100% sales growth
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Exponential growth, logarithmic scale
Exponential demo spreadsheet:
Twelve year, 100% sales growth
http://som.csudh.edu/fac/lpress/netapps/hout/techprogress/exponentialgrowth.xls
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Transistor count – Moore’s Law
Is this linear growth or exponential growth? Explain your answer?
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Is this linear growth or exponential growth? Explain your answer?
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New Yorkers see the world logarithmically
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Summary
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Play around with this exponential demonstration spreadsheet:http://som.csudh.edu/fac/lpress/netapps/hout/techprogress/exponentialgrowth.xls
Moore’s Law article:ftp://download.intel.com/museum/Moores_Law/Articles-Press_Releases/Gordon_Moore_1965_Article.pdf
For more on Moore’s Law, see:http://en.wikipedia.org/wiki/Moore's_law
Wolfram Alpha Moore’s law calculator:http://www.wolframalpha.com/input/?i=moore's+law
Resources
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Self-test questions
Before answering these questions, play around with the spreadsheet at: http://som.csudh.edu/fac/lpress/presentations/exponentialgrowth.xlsx
1. How does the graph change when the original amount is increased from $1,000 to $10,000? To $1? To $1,000,000?
2. What does the graph look like when annual growth is only 1%? 50%? 100$ 300%?3. If sales grows at only 1 percent per year, is that considered exponential growth?4. If plotted on a linear scale, will 1% growth per year be a straight line or a “hockey
stick?”5. If plotted on a logarithmic scale, will 1% growth per year be a straight line or a “hockey
stick?”6. If automobile gas mileage doubled each year, how many miles per gallon would a
typical car get in ten years?7. The first CPU chip had about 2,300 transistors in 1971. A CPU might have 2.3 billion
today. How many times has the number of transistors doubled since 1971?