# Math Help - Just needed help on this one

1. ## Just needed help on this one

I kinda got stuck on this one here.

It says:
Einsteinium (254Es) has a half-life of 270 days. How much of a 5-gram sample would remain after 2160 days?

2. Originally Posted by dc52789
I kinda got stuck on this one here.

It says:
Einsteinium (254Es) has a half-life of 270 days. How much of a 5-gram sample would remain after 2160 days?
recall that $r = \frac {\ln 2}{\text{half life}}$

use that $r$ in the exponential decay formula: $N(t) = N_0e^{-rt}$

where $N(t)$ is the amount remaining after time $t$, $N_0$ is the initial amount, $r$ is the rate of decay

you want to find $N(2160)$

3. Originally Posted by Jhevon
recall that $r = \frac {\ln 2}{\text{half life}}$

use that $r$ in the exponential decay formula: $N(t) = N_0e^{-rt}$

where $N(t)$ is the amount remaining after time $t$, $N_0$ is the initial amount, $r$ is the rate of decay

you want to find $N(2160)$
For r, would it be best if it's nearest to the hundredth or the thousandth?

4. Originally Posted by dc52789
For r, would it be best if it's nearest to the hundredth or the thousandth?
well, that depends on a lot of things. what would your professor want? how many decimal places does your text usually use? etc. follow those guidelines. personally, i use as many decimal places as possible, and then round off my final answer if required

5. Originally Posted by Jhevon
well, that depends on a lot of things. what would your professor want? how many decimal places does your text usually use? etc. follow those guidelines. personally, i use as many decimal places as possible, and then round off my final answer if required
He asked to give the answer to the nearest thousandths of a gram.

6. Originally Posted by dc52789
He asked to give the answer to the nearest thousandths of a gram.
ok, so work with the nearest ten-thousandths and then round it off to the nearest thousandths when finished

7. Originally Posted by Jhevon
ok, so work with the nearest ten-thousandths and then round it off to the nearest thousandths when finished
o k...I have 0.414 as my answer. Is it correct?

8. Originally Posted by dc52789
o k...I have 0.414 as my answer. Is it correct?
that's not what i got

9. Originally Posted by dc52789
I kinda got stuck on this one here.

It says:
Einsteinium (254Es) has a half-life of 270 days. How much of a 5-gram sample would remain after 2160 days?
You don't need logarithms for this. Saying its half-life is 270 days means you multiply by 1/2 every 270 days. 2160/270= 8 so 2160 days is 8 270 day perionds: 5 gms will be multiplied by 1/2 8 times: 5(1/2)^8= 5/256 grams.

10. Originally Posted by HallsofIvy
You don't need logarithms for this. Saying its half-life is 270 days means you multiply by 1/2 every 270 days. 2160/270= 8 so 2160 days is 8 270 day perionds: 5 gms will be multiplied by 1/2 8 times: 5(1/2)^8= 5/256 grams.
wow...that helps a lot. Thanks.