# algebra

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Suppose a sample of Cesium-137 with initial mass of 200 grams decays to a mass of 160 grams voer the course of 10 years.
Find the half-life of Cesium-137 (Round to the nearest year)
How much Cesium-137 is left in the sample after 60 years? Round to the nearest tenth of a gram.

• algebra -

If T is the half life,

(1/2)^(t/T) = 0.16/0.20 = 0.80
where t = 10 yr

(t/T) = 0.3219
T = 31 yr

After 60 yr, the fraction left is
(0.5)^(60/31) = 0.261

Amount left = 200*0.261 = 52.3 g

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