Continuous Exponential Growth

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Continuous Exponential Growth

• PMa 12
• Mr. C. Hunter

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(No Transcript)
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Consider the following unrealistic situation.
1 is invested at 100/a.
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Contd
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As n increases,
approaches 2.718281
Called Eulers number, e
This number is irrational (like p)
log base e is called the natural log, ln
For students taking Calculus 12, this means
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1. Evaluate.
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Did you know?

• Pi day is celebrated by math dorks around the
  world on March 14 (3/14)

• 3/14 happens to be Albert Einsteins birthday

• The Guinness World Record for remembered digits
  of pi is 67 890 digits

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Did you know?

• in the IPO filing for Google, the company
  announced its intention to raise 2,718,281,828,
  which is e billion dollars

• the large number 10100 is called 1 googol

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Any situation where continuous growth occurs at
r/a is given by
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2. The population of a city was 750 000 in 1991.
The population has been growing continuously at
an average rate of 2/a. Find the projected
population in 2011.
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3. The population of a city is 850 000. The
population has been growing continuously at an
average rate of 4/a. How long will it take to
reach 1 million?
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ln e0.04t means logee0.04t