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Topic: Re: e^x
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Mark Howell

Posts: 28
Registered: 12/6/04
Re: e^x
Posted: Feb 24, 1998 2:14 PM
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>Again, this is a unique property of the exponential function. A vertical shift
>is the same as a vertical stretch. So the A and C are different arbitrary
>constants, but if chosen correctly, they will result in the same particular
>solution.
>


Er, you mean a horizontal shift is the same as a vertical stretch?
i.e. e^(x-h) = ke^x, true when k = e^-h.

In Doug's case, Ae^x = e^x+C only when A=1 and C=0 i.e. for e^x.

On a loosely related note, I've use the corresponding property
in logarithms to advantage:

ln(x) + ln(a) = ln(ax)
i.e. a vertical *shift* is the same as a horizontal *stretch*.

The analagous property holds for the exponential, of course,
since "vertical" is translated to "horizontal" when talking
about the inverse function.

Mark Howell
Gonzaga College High School
19 Eye Street NW
Washington, DC 20001 USA
mhowell@gaia.gonzaga.org





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