An anthropologist finds bone that her instruments measure it as 0.717% of the amount of carbon-14 the bones would have contained when the person was alive. how long ago did the person die?
the half life of carbon 14 is 5,730 years. round your answer to the nearest thousand.

Let us find the rate for the general form of y=ar^t.  We are told that the half life is 5730 so we can say:

a/2=ar^(5730)

1/2=r^5730

(1/2)^(1/5730)=r so

y=a(1/2)^(1/5730)^t

y=a(1/2)^(t/5730)

The we are told that 100(y/a)=0.717

y/a=0.00717

and we know that:

y/a=(1/2)^(t/5730) and since y/a=0.00717 we have:

0.00717=(1/2)^(t/5730)  taking the natural log of both sides

ln(0.00717)=(t/5730)ln(1/2)

ln(0.00717)/ln(0.5)=t/5730

t=5730ln(0.00717)/ln(0.5)

t≈40819.43...

t≈41000 years (to the nearest thousand years)

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