An archaeologist unearths the remains of a wooden box, analyzes for the carbon-14 content, and finds that about 93.75% of the carbon-14 initially present has decayed. The half-life of carbon-14 is 5600 years. How old is the box?

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Answer 1 · 2017-11-19T12:56:27

About 41,000 years.

1st order decay gives us:

#sf(N_t=N_0e^(-lambda"t"))#

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Taking natural logs of both sides #sf(rArr)#

#sf(lnN_t=lnN_0-lambda"t")#

#sf(ln(N_t/N_0)=-lambda"t")#

#sf(lambda=0.693/t_(1/2)=0.693/5600=0.00012375color(white)(x)a^(-1))#

#:.##sf(ln(6.25/100)=-0.00012375t)#

#sf(t=(-5.07517)/-0.00012375=41,011color(white)(x)"yr")#