Exponential growth

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Skills: noneConcepts: linear growth, exponential growth, linear scale plot, logarithmic scale plot, “hockey stick,” Moore’s Law, hosting in the cloud

Where does this topic fit?

• Internet concepts– Applications– Technology– Implications

• Internet skills– Application development– Content creation– User skills

Grow by the same amount in each time period

Grow by the same percent in each time period

Linear versus exponential growth

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

Exponential growth, linear scale

Twelve year, 100% sales growth

Exponential growth, logarithmic scale

Exponential demo spreadsheet:

Twelve year, 100% sales growth

http://som.csudh.edu/fac/lpress/netapps/hout/techprogress/exponentialgrowth.xls

Transistor count – Moore’s Law

Is this linear growth or exponential growth? Explain your answer?

Is this linear growth or exponential growth? Explain your answer?

New Yorkers see the world logarithmically

Summary

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

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?