anonymous
  • anonymous
A radioactive isotope has a half life of 700 years. If there is currently 6 mg of the isotope then how much was there 350 years ago? A) 7.74 mg B) 8.49 mg C) 9.24 mg D) 9.99 mg E) 10.74 mg
Mathematics
jamiebookeater
  • jamiebookeater
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yuki
  • yuki
hey, still having trouble with decays ?
yuki
  • yuki
half life problems are the same as the other exponential decay problems , it only focuses on how long it takes so that the size of the object is half.
yuki
  • yuki
so instead of just \[N_t = N_0(R)^{t}\] you can now use \[N_t = N_0(1/2)^{t/h}\]

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yuki
  • yuki
where h is the half life
yuki
  • yuki
so in your problem, the initial amount is what we are looking for and N_t is 6 mg while h =700. \[6 = N_0(1/2)^{350/700}\] t = 350 because 350 years later, the amount is 6mg. in other words, now it is 6mg and we want to know how much it was 350 years ago
yuki
  • yuki
so N_0 is approximately 8.49
yuki
  • yuki
I need to go, so just remember the eqn I taught you, ok? good luck :)

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