>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 email@example.com