Posted by Anonymous on Saturday, January 24, 2009 at 7:40pm.
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?

Math  Exponential Decay  Damon, Saturday, January 24, 2009 at 7:51pm
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

Math  Exponential Decay  bobpursley, Saturday, January 24, 2009 at 7:53pm
your calculator. Set it on scientific, so the k is equal to 4.101E4
With that, I get 5615 years.

Math  Exponential Decay  DrBob222, Saturday, January 24, 2009 at 7:57pm
I, too, get 5615.
Answer This Question
Related Questions
 Chem 3A  please help me with this chemistry problem. HalfLife A radium226 ...
 Calculus  Radius decays at a rate of that is proportional to its mass, and has ...
 Math  In 1976 a research hospital bought half a gram of radium for cancer ...
 Math  In 1976 a research hospital bought half a gram of radium for cancer ...
 chemistry  A radium226 sample initially contains 0.112mol. How much radium226...
 physics  The half life period of radium is 1600 years.In how many years 1 gram ...
 Pre Calculus  Radium221 has a halflife of 30 s. How long will it take for 95...
 Chemistry  Radium223 has a halflife of 11.4 days.Approximately how long would...
 help  the halflife of a radium is 1690 years is 90 grams is present now, how ...
 Science  Radium has a halflife of 1620 years and decays into radon, which has...
More Related Questions