On the web (ie, Wikipedia, and other sites) it seems that exponential decay is always defined as the situation $f\;'(t) = -kf(t)$. However, is not Newton’s Law of Cooling an example of exponential decay? But Newton’s Law of Cooling does not fit this form. What is missing is a constant. If we define exponential decay to be the situation $f'(t) = w - kf(t)$, then everything’s fine. So, is there in fact a constant missing (for convenience?) from the widely-disseminated definition of exponential decay, or, as I suspect, is the definition not all that fixed, depending on some judicious arm-waving as the occasion demands?
What is exponential decay, exactly?
1
$\begingroup$
calculus
-
2If you say that $f(t)$ is the difference, at time $t$, between the object's temperature and the temperature of the surroundings, then Newton's law of cooling _does_ fit that form. – 2011-10-19
-
0@Michael Hardy: Bingo. THAT answers my question. I'm shamefaced I didn't notice it myself. Anyway, if you will post your comment as an answer, I will accept it. – 2011-10-19