Question

How to write a half-life function?

I am working on a project for math and one of the things I have to do is write a half-life function with the data I came up with. I looked all through my book and can't even find a mention of the term.

Answer 1

Here is the data I have to write the function based off of

Answer 2

The half-life is the period of time it takes to fall to half of its value. But looking at your table, I don't quite see how that applies here...

Answer 3

Are your various trials supposed to represent measurements of the remaining quantity in identical samples after an identical amount of time?

Answer 4

Oh i see what I did wrong!!! Let me attach another table...

Answer 5

Ah, that makes more sense! :-)

Answer 6

Yes! I re-read the instructions and saw I was supposed to eliminate objects...

Answer 7

@whpalmer4

Answer 8

Sorry, openstudy is being a bit flaky for me :-(

So your data looks like this when plotted (I'm plotting the number of coins still face up vs. the trial number, assuming the trial number is equivalent to elapsed time):

Answer 9

To find the half-life, you need to fit the right sort of curve through those points, and determine how much time has to elapse to cut the initial quantity in half

Answer 10

@whpalmer4

Answer 11

simplest way is using the function.

it is in the form:

\[f(x) = f(0)e^{-ax}\]

f(0) is the initial amount (when x = 0). so the half-life is when f(x) = f(0)/2

re-written:

\[\frac{ f(0) }{ 2 }= f(0)e^{-0.61x}\]

re-written:

\[\frac{ 1 }{ 2 } = e^{-0.61x}\]
\[\ln(1/2) = -0.61x\]

x is the half-life amount

Answer 12

@Euler271 Do i simplify further or leave it like that?

Answer 13

Actually, I think your time series should be 20, 13, 8, 5, 3, 1 as 20 is the initial amount — trial 0 is the amount remaining after 1 sampling period has elapsed

Answer 14

you would simplify to find x