Curse

Taisayacho · May 28, 2008, 06:26 PM // 18:26

If a substance, a 100g sample, has a half-life of 40 minutes. what's the equation for the half life?
How about 40 hours?
Thanks!
(If there isn't an equation, sorry)

Turbobusa · May 28, 2008, 06:37 PM // 18:37

http://en.wikipedia.org/wiki/Biological_half-life
from what I read it depends on "the initial concentration of the drug A0" and is "inversely proportional to the zero-order rate constant k0"
So you can't really calculate the sample size to get a half life of 40h without knowing which substance it is and its properties.

http://en.wikipedia.org/wiki/Half-life
From this one it would only depend on the decay constant lambda.

Taisayacho · May 28, 2008, 06:52 PM // 18:52

The latter is what I'm looking for. I'm pretty sure it can be calculated based on looking at graphs I've gotten in physics but I don't know how you use lambda in that equation on wikipedia.

Turbobusa · May 28, 2008, 11:59 PM // 23:59

Well the formula in the second article allows n you to calculate it from graphs, yes.
You have a whole article there: http://en.wikipedia.org/wiki/Decay_constant
about lambda, but I don't feel like doing diff equations at 2 :P I'll let you read that

bhavv · May 29, 2008, 12:39 AM // 00:39

*brain explodes*

Kattar · May 29, 2008, 06:16 PM // 18:16

Interesting, I thought half life was unrelated to the amount of material present. Guess it makes sense that it's not that way though.

Lord Sojar · May 29, 2008, 06:32 PM // 18:32

Half life always is based on that amount of material present, and its decay rate; Lambda being the decay constant.

Also remember, when a material decays, it produces another material as it loses it own physical state. Best of luck.

The equation would be as follows btw:

40= ln(2)/lambda

However, I believe you want to use the mass equation, or at least that is what I gather.

m(t) = m(0) x 5^(t/t(1/2))

m(t) = the mass after the total time has passed

m(0) = the initial starting mass, in this case 100.

t= time

t(1/2) = the half life of the material, in this case, 40

So, after filling that in, guess what?

m(t)=100 x .5^(t/40)

Make sense? So now you can plugin a value for time, like... 120 minutes, and solve the equation. Hope that helps.

Turbobusa · May 29, 2008, 06:39 PM // 18:39

Apparently it is unrelated, but you can calculate the "time left"; I guess it is before half life.

edit: Ho ok I thought M(t) was the the biological property strength left or something in those lines, not the actual mass. Thanks for clearing that up.

Taisayacho · May 29, 2008, 07:47 PM // 19:47

Hmm I think Rahja has answered me. What I really wanted to know this for is because I was trying to figure out the equation for damage after armor.
Since you take half damage every extra 40 armor, I thought the half life would be 40. Am I right? lol

Turbobusa · May 29, 2008, 09:50 PM // 21:50

So m(t) = m(0) x .5^(t/t_0.5)

t_0.5 "half life" = half damage armor modifier
t = actual armor modifier
m(0) = damage before armor
m(t) = damage after armor?

Wiki states another equation (relative to 60 armor, but the half life equation give the percentage of damage increase/decrease for a said armor modifier).

A 25AL modifier gives m(t) = m(0) . 0.64842, compared to 64.8% from thewiki table.

20 AL, 0.7071 (or 0.5^0.5) compared to 70.7%.

So I guess you were right.

edit: btw source: http://wiki.guildwars.com/wiki/Damage_calculation