有關微積分的問題,這題怎麼算?
2016-01-08 2:47 pm
The amount of a certain radioactive substance remaining after t years is given by a function of the form Q(t)=Qe^-0.003t.Find the half-life of the substance.
回答 (1)
2016-01-08 11:24 pm
✔ 最佳答案
Q(t)=Qe^-0.003tbut Q(t) is also
Q(t)=Q*2^(-t/L)
where L=half life
so equate
Q*2^(-t/L)=Qe^(-0.003t)
cancel Q and take ln
(-t/L)(ln(2)=-0.0003t
cancel -t and solve for L
L=ln(2)/0.0003
=(10000/3)(ln(2))
Check: Q(L)=Q((10000/3)/ln(2))=0.5000Q ok.
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原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20160108064736AAKL84f