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HelpMe94
 3 years ago
What does the Exponential Decay Variables Mean?
For Half Lifes
Y=Ae^bX
HelpMe94
 3 years ago
What does the Exponential Decay Variables Mean? For Half Lifes Y=Ae^bX

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campbell_st
 3 years ago
Best ResponseYou've already chosen the best response.1ok 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

HelpMe94
 3 years ago
Best ResponseYou've already chosen the best response.0Another 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?

HelpMe94
 3 years ago
Best ResponseYou've already chosen the best response.0so normal time is the amount of time passed?

campbell_st
 3 years ago
Best ResponseYou've already chosen the best response.1so 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

HelpMe94
 3 years ago
Best ResponseYou've already chosen the best response.0ok so is 1/2 the grams?

HelpMe94
 3 years ago
Best ResponseYou've already chosen the best response.0also if it is then why is it divided by 1

campbell_st
 3 years ago
Best ResponseYou've already chosen the best response.1well 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

campbell_st
 3 years ago
Best ResponseYou've already chosen the best response.1the calculation is \[\ln(\frac{1}{2}) = b \times 5715\]

HelpMe94
 3 years ago
Best ResponseYou've already chosen the best response.0i see that but what i don't understand is the 1/2

campbell_st
 3 years ago
Best ResponseYou've already chosen the best response.1half 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.

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

HelpMe94
 3 years ago
Best ResponseYou've already chosen the best response.0oh 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...

campbell_st
 3 years ago
Best ResponseYou've already chosen the best response.1thats it... b will be a positive decimal...

HelpMe94
 3 years ago
Best ResponseYou've already chosen the best response.0ok let me see if this checks out for a second

HelpMe94
 3 years ago
Best ResponseYou've already chosen the best response.0one thing were did A go?

campbell_st
 3 years ago
Best ResponseYou've already chosen the best response.1the ratio of Y/A = 1/2
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