Question

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

Answer 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

Answer 2

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?

Answer 3

so normal time is the amount of time passed?

Answer 4

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

Answer 5

thats correct.

Answer 6

ok so is 1/2 the grams?

Answer 7

also if it is then why is it divided by 1

Answer 8

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

Answer 9

give me a moment...

Answer 10

the calculation is

\[\ln(\frac{1}{2}) = -b \times 5715\]

Answer 11

i see that but what i don't understand is the 1/2

Answer 12

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.

Answer 13

so if you really don't need to know the initial quantity if you know how long it takes to get 1/2 life...

Answer 14

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...

Answer 15

thats it...

b will be a positive decimal...

Answer 16

ok let me see if this checks out for a second

Answer 17

one thing were did A go?

Answer 18

oh wait i see

Answer 19

y/a is 1/2

Answer 20

the ratio of Y/A = 1/2