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

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campbell_stBest ResponseYou've already chosen the best response.1
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
 one year ago

HelpMe94Best ResponseYou've already chosen the best response.0
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?
 one year ago

HelpMe94Best ResponseYou've already chosen the best response.0
so normal time is the amount of time passed?
 one year ago

campbell_stBest ResponseYou've already chosen the best response.1
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
 one year ago

HelpMe94Best ResponseYou've already chosen the best response.0
ok so is 1/2 the grams?
 one year ago

HelpMe94Best ResponseYou've already chosen the best response.0
also if it is then why is it divided by 1
 one year ago

campbell_stBest ResponseYou've already chosen the best response.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
 one year ago

campbell_stBest ResponseYou've already chosen the best response.1
the calculation is \[\ln(\frac{1}{2}) = b \times 5715\]
 one year ago

HelpMe94Best ResponseYou've already chosen the best response.0
i see that but what i don't understand is the 1/2
 one year ago

campbell_stBest ResponseYou've already chosen the best response.1
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.
 one year ago

campbell_stBest ResponseYou've already chosen the best response.1
so if you really don't need to know the initial quantity if you know how long it takes to get 1/2 life...
 one year ago

HelpMe94Best ResponseYou've already chosen the best response.0
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...
 one year ago

campbell_stBest ResponseYou've already chosen the best response.1
thats it... b will be a positive decimal...
 one year ago

HelpMe94Best ResponseYou've already chosen the best response.0
ok let me see if this checks out for a second
 one year ago

HelpMe94Best ResponseYou've already chosen the best response.0
one thing were did A go?
 one year ago

campbell_stBest ResponseYou've already chosen the best response.1
the ratio of Y/A = 1/2
 one year ago
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