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| Math Central | Quandaries & Queries |
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Question from Christy, a student: Hello, how do I go about answering this question? Should I be using the formula Ce^(kt)? Given that the decay constant for Radium is -.000428/year, how long, to the nearest year, does it take a sample to decay to 15% of its present mass? |
Hi Christy,
Suppose you have a mass of $C$ units of a radioactive material with decay constant $k$ where the time is measured in year. After $t$ years the mass $A$ of radioactive material remaining is given by
\[A = C e^{k \; t}\]
You are told that for Radium, $k = -0.000428$ and hence
\[A = C e^{-0.000428 \; t}\]
You are asked to find the time $t$ when $A = 0.15 C.$
Substitute $A$ into the equation above and solve for $t.$
Penny
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