Question: Assume that the rate at which radioactive nuclei decay is proportional to the number of such nuclei that are present in a given sample. In a certain sample 10% of the orig. number of radioactive nuclei have undergone disintegration in a period of 100 yrs.
a) what % of the orig. radioactive nuclei will remain after 1000 years

I used the diff eq. dx/dt = -kx
separating this to obtain x=x.e^(-kt) , where x. = orig. sample

at the end I got 0.3486 or 34.86% and book says 59.05%, why????

Question

Question: Assume that the rate at which radioactive nuclei decay is proportional to the number of such nuclei that are present in a given sample. In a certain sample 10% of the orig. number of radioactive nuclei have undergone disintegration in a period of 100 yrs. 
a) what % of the orig. radioactive nuclei will remain after 1000 years

I used the diff eq. dx/dt = -kx
separating this to obtain x=x.e^(-kt) , where x. = orig. sample

at the end I got 0.3486 or 34.86% and book says 59.05%, why????

anonymous · Answer

x=Ae^(-kt)

anonymous · Answer

0.9A=Ae^(-100k)

anonymous · Answer

from the first sentence.

anonymous · Answer

ln(0.9) = -100k

k= 0.0010536....

anonymous · Answer

x = A e^(-kt)   ----> restating the eqn

anonymous · Answer

when t=1000, x= A e^(-0.0010536 x 1000) = A x (0.34868...)

anonymous · Answer

You are correct, there is a mistake with the book.

anonymous · Answer

it still gives me 0.3486 and the book says 0.5905 :s  I think the book is incorrect, then.