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HelpMe94
Group Title
What does the Exponential Decay Variables Mean?
For Half Lifes
Y=Ae^bX
 one year ago
 one year ago
HelpMe94 Group Title
What does the Exponential Decay Variables Mean? For Half Lifes Y=Ae^bX
 one year ago
 one year ago

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campbell_st Group TitleBest 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

HelpMe94 Group TitleBest 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

HelpMe94 Group TitleBest ResponseYou've already chosen the best response.0
so normal time is the amount of time passed?
 one year ago

campbell_st Group TitleBest 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

campbell_st Group TitleBest ResponseYou've already chosen the best response.1
thats correct.
 one year ago

HelpMe94 Group TitleBest ResponseYou've already chosen the best response.0
ok so is 1/2 the grams?
 one year ago

HelpMe94 Group TitleBest ResponseYou've already chosen the best response.0
also if it is then why is it divided by 1
 one year ago

campbell_st Group TitleBest 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

HelpMe94 Group TitleBest ResponseYou've already chosen the best response.0
give me a moment...
 one year ago

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

HelpMe94 Group TitleBest 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_st Group TitleBest 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_st Group TitleBest 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

HelpMe94 Group TitleBest 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_st Group TitleBest ResponseYou've already chosen the best response.1
thats it... b will be a positive decimal...
 one year ago

HelpMe94 Group TitleBest ResponseYou've already chosen the best response.0
ok let me see if this checks out for a second
 one year ago

HelpMe94 Group TitleBest ResponseYou've already chosen the best response.0
one thing were did A go?
 one year ago

HelpMe94 Group TitleBest ResponseYou've already chosen the best response.0
oh wait i see
 one year ago

HelpMe94 Group TitleBest ResponseYou've already chosen the best response.0
y/a is 1/2
 one year ago

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