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

Radium decays exponentially. Its half-life is 1,690 years. How long will it take for a 50-gram 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 4.101E-4

With that, I get 5615 years.

- Math - Exponential Decay -
**DrBob222**, Saturday, January 24, 2009 at 7:57pm
I, too, get 5615.

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