Math CentralQuandaries & Queries


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 $t.$


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