Pronunciation: /ˈdʌ.blɪŋ taɪm/ Explain
Click on the blue points on the sliders and drag them to change the figure.|
How does the doubling time change when a changes? Why? How does the doubling time change when b changes? Why?
|Manipulative 1 - Doubling Time Created with GeoGebra.||
Doubling time is the amount of time it takes for an
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
- How does the doubling time change when a changes? Why?
- 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:
is the interest rate.
How to Calculate Doubling Time
Doubling time can be calculated given any exponential equation in the form
this equation, there exists an equation of the form
equivalent to .
Since the base of the second equation is 2, it doubles every time c
increases by 1. So c is the doubling time.
||Since y = y, the right
hand sides of the two equations are equal to each other.|
||Divide both sides by a, eliminating it from the equation. A
consequence of this step is that a != 0.|
||Use the definition of logarithm to transform the equation.|
||Use the power rule of logarithms to pull cx out of the logarithm.|
||Divide both sides by x, eliminating it from the equation. A
consequence of this step is that x != 0.|
||Transform the log base d to the natural log using the change of
||Divide both sides by the logarithmic ratio. c is now on one side
of the equation by itself. What is on the right hand side of the equation is
the doubling time.|
|Table 1: Derivation of doubling time.|
- McAdams, David E.. All Math Words Dictionary, doubling time. 2nd Classroom edition 20150108-4799968. pg 67. Life is a Story Problem LLC. January 8, 2015. Buy the book
- Rule of 72. investopedia.com. Investopedia. Forbes Digital. Last Accessed 7/3/2018. http://investopedia.com/terms/r/ruleof72.asp.
- Lodge, Sir Oliver. Easy Mathematics; or, Arithmetic and Algebra for General Readers. pp 353-356. www.archive.org. Macmillan and Company. 1910. Last Accessed 7/3/2018. http://www.archive.org/stream/easymathematicso00lodguoft#page/353/mode/1up. Buy the book
- Math 120 Book. pp 698-699. www.archive.org. Last Accessed 7/3/2018. http://www.archive.org/stream/Math120Book-Entire/Math120-fullBook#page/n334/mode/1up/search/doubling.
Cite this article as:
McAdams, David E. Doubling Time. 4/20/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/d/doublingtime.html.
4/20/2019: Updated equations and expressions to the new format (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
7/4/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
12/16/2008: Initial version. (McAdams, David E.)