作者Honor1984 (希望愿望成真)
看板trans_math
标题Re: [考古] 96实践转学考 微积分题目...
时间Thu Jul 10 12:42:23 2008
※ 引述《love606009 (Jay~^^)》之铭言：
: 某一题...
: A radioactive isotope has a half-life of 40 years. at=0,there are 200 grams of
: this substance. find the amount of this isotope present at time t using an
: exponential model of decay.
: 这题我完全看不出来後半段再描述什麽...无法下笔
exponential model
dn/dt = -kn
=> ln(n) = -kt + C
=> n = Aexp(-kt)
n(0)= N = 200(gram)
=> N = A*1 = A
=> n = Nexp(-kt)
half life t'
(1/2)N = Nexp(-kt')
=> -ln2 = -kt'
=> t' = ln2 / k
For t' = 40(year) = ln2 / k
=> k = t'/ln2 = ln2 /40 (1/year)
=> n(t) = Nexp(-kt) = 200exp(-tln2 /40)
= 200 * (1/2)^(t/40) (gram)
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