Note thatP(2) = 40 andP(4) = 120, we obtain40 =P(0)e2k,120 =P(0)e4k.These imply thatP(0) =403ande2k= 3,ork= ln 3/2.We thus haveP(t) =4033t/2=403√3t=403e(ln 3/2)t.Example.The half-life of Sodium-24 is 15 hours. Suppose you have 100 grams of Sodium-24. How many grams remaining after 27 minutes (keep three decimals)?
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Example.Use Newton’s Law of Cooling to determine the time of death of a healthy man.•He died in his room some time before noon;•At noon, his body temperature was found to be 70 degrees;•His body cooled another 5 degrees in 1 hour after noon;•The room temperature was a constant 60 degrees;•Normal temperature of people’s body is 98.6 degree.
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