<span>The relative rate of change of a function f(x) is the ratio of the derivative f'(x) to the function f(x).
Since f'(x) = -4e^(-2x) the relative rate of change r = [-4e^(-2x)]/[12 + 2e^(-2x)].
This can be simplified by factoring a value of two resulting in:
r = [-2e^(-2x)]/[6 + e^(-2x)].
This can be further re-arranged if desired into:
r = -1/3 e^(-2x) - 2</span>
The rate of change of a given function is given by f'(x)=dy/dx given that the function is: f(x)=12+2^(-2x) f'(x)=2*(-2)e^(-2x) f'(x)=-4e^(-2x) the relative rate of change will be the ratio of the derivative to the original function: f'(x)/f(x) =(12+2^(-2x))/(-4e^(-2x))
