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HelpMe94
What does the Exponential Decay Variables Mean? For Half Lifes Y=Ae^-bX
ok so your formula is A is the initial population b is the decay coefficient X is normally the time. \[Y = Ae^{-bx}\] then 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 \[\frac{1}{2} = e^{-bX}\] you can find - bX by taking the log of both sides of the equation
Another thing is if i know the half life in years = 5715 and the amount after 1000 years is 2 grams then what is the initial amount?
so normal time is the amount of time passed?
so then X = 5715 this will help to find the decay constant - b \[\frac{1}{2} = e^{-b \times 5715}\] you'll need to solve for b by using logs... the when you have b you will be able to find A given Y = 2 and X = 1000
ok so is 1/2 the grams?
also if it is then why is it divided by 1
well half life means you end up with 1/2 of what you start with... and because you are given X = 5715 you can calculate b
the calculation is \[\ln(\frac{1}{2}) = -b \times 5715\]
i see that but what i don't understand is the 1/2
half life if you start with 100 gm then 50gm is the half life, 20gm then 10gm is the half life. 3 gm then 1.5 gm is the half life. so its when the initial quantity gets to half its size.
so if you really don't need to know the initial quantity if you know how long it takes to get 1/2 life...
oh so is 1/2 just to solve to get b then plug in to the equation for the 1000 years =x to get the answer...
thats it... b will be a positive decimal...
ok let me see if this checks out for a second
one thing were did A go?
the ratio of Y/A = 1/2