radioactive carbon-14 decays according to the functionQ(t)=Q(initial)e^-0.000121
ID: 3091996 • Letter: R
Question
radioactive carbon-14 decays according to the functionQ(t)=Q(initial)e^-0.000121t where t is the time in years, Q(t) isthe quantity remaining at time t, and Q(initial) is the amountpresent at time t=0.estimate the age of a skull if 23% of theoriginal quantity of carbon-14 remains. at first i thought this was sort of a plug and chug equationbut the skull be thrown into it confused me, need help radioactive carbon-14 decays according to the functionQ(t)=Q(initial)e^-0.000121t where t is the time in years, Q(t) isthe quantity remaining at time t, and Q(initial) is the amountpresent at time t=0.estimate the age of a skull if 23% of theoriginal quantity of carbon-14 remains. at first i thought this was sort of a plug and chug equationbut the skull be thrown into it confused me, need helpExplanation / Answer
The skull is just the setting, to make this a "practical"problem; the word is there to point out that this math hasimportant applications in the real world. The backstory tothis problem is that an archaeologist or paleontologist hasdiscovered some sort of skull that was buried a very, very, verylong time ago, and he wants to know approximately how long agoit was. The way he does this is to look at how much carbon-14has decayed since the skull was buried. If you ever see newsstories saying something like "65,000 year-old woman found," thisis the method they probably used to figure out that date. . If you were trying to be an archaeologist, these details wouldmatter. For your purposes, you can ignore the fact thatthere's a skull in this problem and just plug and chug. Q(initial) is 100% of the carbon that was originally in the skull;Q(t) is 23% of the carbon. You need to figure out what tis. . (Note that carbon 14 is used for dating things that are reallyreally old. The basic math is also important forunderstanding nuclear physics, criminal forensics, and banking,among many many other applications. Exponential growth modelsare very important!)Related Questions
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