SOLUTION: Cesium 137 is a radioactive metal with a short half-life of 30 years. In a sample originally having 1 gram of cesium 137, the amount of cesium 137 present after t years is given b

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Question 1190552: Cesium 137 is a radioactive metal with a short half-life of 30 years. In a
sample originally having 1 gram of cesium 137, the amount of cesium 137 present after t years is given by A(t) = (1/2)^t/30. where A is the amount of cesium in grams and t is the time in years.
a. How much cesium 137 will be present after 30 years?
b. How much cesium 137 will be present after 90 years?
Answer by ikleyn(52803) About Me  (Show Source):
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Cesium 137 is a radioactive metal with a short half-life of 30 years. In a
sample originally having 1 gram of cesium 137, the amount of cesium 137 present after t years is given by
A(t) = (1/2)^t/30. where A is the amount of cesium in grams and t is the time in years.
a. How much cesium 137 will be present after 30 years?
b. How much cesium 137 will be present after 90 years?
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(a)  30 years is one half-life.


     THEREFORE, the remaining mass of the 1 gram of cesium-137 after 30 years is  1%2F2 = 0.5 grams.


     You will get the same answer, if you substitute the value t= 30 years into the given exponential decay function.





(b)  90 years is 3 (three) half-lives.


     THEREFORE, the remaining mass of the 1 gram of cesium-137 after 90 years is  %281%2F2%29%5E3 = 1%2F2%5E3 = 1%2F8 = 0.125 grams.


     You will get the same answer, if you substitute the value t= 90 years into the given exponential decay function.

Solved.

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On radioactive decay,  see the lesson
    - Radioactive decay problems
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    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic "Logarithms".


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