Help with Half-Life! (math problem :/)

If it's purely a math problem (which it most likely is not, and I'm probably totally wrong), then it would take 13 years for 50% of these 10 grams to dissapear.
Therefore, in one year it would deteriorate (50/13 = approx) 4%. In two years, it would then deteriorate 8%, leaving 92% of the original 10 grams (9,2 grams).

However, I'm fairly certain that's not how half-life works, so you know :P

Okay OP, a half life means that half of a substance will have depleted in that period of time. In this case, it's 13 years. So 10g of Pultonium-241 will have depleated in 13 years leaving 5g correct? So, to figure out the amount decayed in only 2 years, set the problem up so that you figure out just 2 years worth the 13 year half life (ie: 2/13)
Basically, you can do it like this: 10(1-(0.5(2/13)))= 9.230769g still remain after 2 years.~

Edit: Crap that's set up as a linear function, not an exponential function. That was completely incorrect. You need to figure it out following what idw4890 posted below.

You'd lose 0.76923 grams. Half-life of 13 years means that after 13 years you'd be left with half the plutonium you had at the start. After 2 years only 2/13 of that half could decay. So 10-((2/13)0.5)10)
EDIT: or not clicky

You will need to use the half like formula to solve the problem, since half life follows an exponential decay, NOT a linear one. Usually the formula is given by N=(N_0)e^(kt) where N_0 is the initial amount (here its 10), k is the decay constant, and t is the time. First you will need to solve for k (it should be negative), then plug in that value along with t=2 and N_0 of 10 in the half life formula to solve for N, the current amount left after two years have passed.

If I remember correctly, half-life has a exponencial decay of base 2 so the percentage remaining after N half-life cycles have passed is given by 1/(2^N). Here N is 2/13. Since you have 10 grams in the beggining after 2 years you will have 10/(2^(2/13))=8.9885 grams.

Let's denote the part of the plutonium that does NOT decay after a year with x. After a year, the 10 gram will be x 10g. After two years, it will be x x 10g, etc.
After 13 years, it is x x x ... (13 times) ^13, but that is equal to the half-life, so it is x^13 10g = 0.5 10g
Out of that, you can conclude, that x = 13-root(0.5) = 0.5^(1/13).
But you need 2nd year, where the same part will decay: x x 10g = x^2 10g = (0.5^(1/13))^2 10g = [8.989 grams](http://www.wolframalpha.com/input/?i=%280.5^%281%2F13%29%29^2++10g)