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Th half-life of Carbon 14 is 5730 years. If 8 grams remain after 1000 years, what was the initial quantity?
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Exponential decay is described by:
N(t) = N(0) e^(kt)
where
N(t) amount at time t
N(0) initial amount
k is the growth rate
t is time
.
First we need to figure out what k is...
x/2 = x * e^(5730k)
1/2 = e^(5730k)
ln(1/2) = 5730k
ln(1/2)/5730 = k
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Now, we can answer:
If 8 grams remain after 1000 years, what was the initial quantity?
N(t) = N(0) e^(kt)
Let x = initial quantity
8 = x * e^(1000 * ln(1/2)/5730)
8/e^(1000 * ln(1/2)/5730) = x
9.03 grams = x
