Question

What does the Exponential Decay Variables Mean? For Half Lifes Y=Ae^-bX

Answer 1

A is the initial population
 
b is the decay coefficient
 
X is normally the time.

$Y = Ae^{-bx}$

then is the population half of the initial population of A
 
for half life you will have

$\frac{Y}{A} = \frac{1}{2}$

so the equation becomes

$\frac{1}{2} = e^{-bX} \\ \\\ln{ \frac{1}{2}} =\ln{e^{-bX}} \\ \\ \ln{1}-\ln{2}=-bX \\bX=\ln{2}$