Re: exponential equation with constant

Let's see. Using your trick of letting y = exp(-ct), assuming c != 0,
yields

b*(y^(d/c)) + a*y - 1 = 0.

The means of solution will now depend on the nature of d/c. If it
happens to be 2, you have a quadratic equation and are good to go. If
it is 3 or 4 there are exact solutions. Otherwise you need, not a
computer simulation, but an iterative algorithm that will solve the
equation. These should be pretty easy to come up with, or else you
could just use the good old Newton-Raphson. I suppose you could study
some theoretical issues like existence and uniquess as well as location
interms of a, b, and d/c without using computational techniques, but
for most values of d/c you will need to use computational techniques do
determine a good approximation to the solution (or solutions).

Regards,
Achava

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