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May 26, 2015

Homework Help: word problem

Posted by Jen on Wednesday, February 14, 2007 at 9:39am.

The half life of cesium-137 is 30 years. Suppose we have a 10-g sample.
a)Find a function that models the mass remaining after t years.
b)How much of the sample will remain after 80 years?
c)After how long will only 2 g of the sample remain?

Thanks

(a) M(t) = mass of Cesium-137 at time t, in years = Mo* 2^(-t/30)
Mo is the initial mass of 10 g.
2^(-t/30) means 2 to the -t/30 power

(b) Plug in t = 80 and see that you get for M

(c) Set M = 2 and see what you get for t. Hint: take logs of both sides of:
2 = 10 * 2^(-t/30)
(0.2) = 2^(-t/30)

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