Exponential growth This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License. Skills: none Concepts: linear growth, exponential growth, linear scale plot, logarithmic scale plot, “hockey stick,” Moore’s Law, hosting in the cloud

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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

Year Growth % % % % Exponential growth

Exponential growth, linear scale Twelve year, 100% sales growth

Exponential growth, logarithmic scale Exponential demo spreadsheet: Twelve year, 100% sales growth

Transistor count – Moore’s Law Is this linear growth or exponential growth? Explain your answer?

New Yorkers see the world logarithmically

Summary

Play around with this exponential demonstration spreadsheet: ialgrowth.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: Wolfram Alpha Moore’s law calculator: Resources

Self-test questions Before answering these questions, play around with the spreadsheet at: 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 A CPU might have 2.3 billion today. How many times has the number of transistors doubled since 1971?