SOLUTION: This is exactly how my teacher asked this question. A radioactive element decays at a rate of 7%. What is the half-life of the element (exact answer).

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Question 1006964: This is exactly how my teacher asked this question.
A radioactive element decays at a rate of 7%. What is the half-life of the element (exact answer).
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A radioactive element decays at a rate of 7%. What is the half-life of the element (exact answer).
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No time units are given, so it's 7% per unit time.
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Remaining amount A(t) = A(o)*0.5^(t/HL) ----- A(o) = Original amount
A(t)/A(o) = 0.93 = 0.5^(1/HL)
ln(0.93) = (1/HL)*ln(0.5)
1/HL = ln(0.93)/ln(0.5)
Half life = ln(0.5)/ln(0.93) time units