Find X in plateau of exponential decay

Question

I have this equation:

$$y=(a+b)\cdot e^{-KX} + c.$$

This is an exponential decay function.

I need to get its derivative and find $X$ when derivative $= 0$. This function has a plateau at $y = c$. In other words, I want to find when $X$ reaches the plateau (c) when the gradient of this curve is $0$. Is it even possible?

I can't get around it.

Thank you

Answer 1

Hint: The derivative of $e^{-KX}$ is $-KX e^{-KX}$. Set your $f'(X)=0$, re-arrange your equations and then take logs of both sides of the equation to solve for $X$.