Doubling Time

Pronunciation: /ˈdʌ blɪŋ taɪm/ ?

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Manipulative 1: Doubling Time. Created with GeoGebra.

Doubling time is the amount of time it takes for an exponential function to double. If an exponential function goes from 1 to 2 in 10 seconds, it will go from 2 to 4 in 10 seconds and 4 to 8 in 10 seconds. An exponential function always doubles in the same amount of time.

Manipulative 1 illustrates doubling time for an exponential function of the form
f(x)=a*e^(b*x).
Click on the blue points on the sliders and drag them to change the equation for the graph.

Discovery

  1. How does the doubling time change when a changes? Why?
  2. How does the doubling time change when b changes? Why?

Rule of 72

The rule of 72 can be used to approximate doubling time of investments at a given interest rate. The rule of 72 states:
t=0.72/r
where r is the interest rate.

References

  1. Rule of 72. investopedia.com. Investopedia. Forbes Digital. (Accessed: 2010-01-05). http://investopedia.com/terms/r/ruleof72.asp.
  2. Lodge, Sir Oliver. Easy Mathematics; or, Arithmetic and Algebra for General Readers, pp 353-356. Macmillan and Company, 1910. (Accessed: 2010-01-24). http://www.archive.org/stream/easymathematicso00lodguoft#page/353/mode/1up.
  3. Math 120 Book, pp 698-699. (Accessed: 2010-01-24). http://www.archive.org/stream/Math120Book-Entire/Math120-fullBook#page/n334/mode/1up/search/doubling.

Cite this article as:


Doubling Time. 2010-01-24. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/d/doublingtime.html.

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Revision History


2008-12-16: Initial version (McAdams, David.)

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