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Half Life Formula Math. Take the natural log of both sides to get k out of the exponent: N t = mass of radioactive material at time interval (t).
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N 0 = mass of the original amount of radioactive material. Solve for the decay rate k: Take the natural log of both sides to get k out of the exponent:
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To find k, let \(a(t)=a_o/2\), \(t=1690\) and solve for k. Learn the formula for half life as well as see an example in this free math video tutorial by mario's math tutoring.0:09 formula for calculating half life0:3. Make sure you find the initial value for each equation. Start by dividing both sides by the coefficient to isolate the exponential factor: