SOLUTION: If 250 mg of a radioactive element decays to 230 mg in 12 hours, find the half-life of the element. (Round your answer to the nearest whole number.) ______hr

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: If 250 mg of a radioactive element decays to 230 mg in 12 hours, find the half-life of the element. (Round your answer to the nearest whole number.) ______hr      Log On


   

Question 1026381: If 250 mg of a radioactive element decays to 230 mg in 12 hours, find the half-life of the element. (Round your answer to the nearest whole number.)
______hr
Answer by robertb(5830) About Me  (Show Source):
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For exponential decay/growth the basic model is P=P%5B0%5De%5E%28rt%29+=+250e%5E%28rt%29.
After 12 hours, the equation becomes 230+=+250e%5E%2812r%29
==> 0.92+=+e%5E%2812r%29 ==> ln0.92 = 12r, or r+=+ln0.92%2F12.
==> , or
P+=+250%2A.92%5E%28t%2F12%29.
To find the half-life set P=125 (half of 250.)
==> 125+=+250%2A.92%5E%28t%2F12%29.
==> 0.5+=+0.92%5E%28t%2F12%29 ==> t+=+-12log2%2Flog0.92
==> t = 99.8, or 100 hours, rounded off to the nearest whole number.