Math  Exponential Decay
posted by Anonymous on .
Radium decays exponentially. Its halflife is 1,690 years. How long will it take for a 50gram sample of radium to be reduced to 5 grams?
1/2P = Pe^(1690k)
(ln1/2)/(1690) = k
4 x 10^4 = k
5 = 50e^kt
ln0.1 = kt
ln0.1/k = t
5,630 years = t
...but textbook answer is 5,614 years. Where did I go wrong?

I got 5616 using 4.1 * 10^4 for k
You did it right but did not carry the same number of significant figures.
it is easier to use a^b = 1/a^b in a case like this
1/10 = e^kt
becomes
e^kt = 10
t = ln 10/k = 2.303/.00041 
your calculator. Set it on scientific, so the k is equal to 4.101E4
With that, I get 5615 years. 
I, too, get 5615.