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blondinia [14]
3 years ago
8

Carbon-14 decays at a constant rate, so it can be used to determine the age of fossils. In particular, if the original amount of

Carbon-14 present is A0, then A(t) = A0e^(-kt) can be used find the amount of amount of Carbon-14 remaining after t years. Given that the half-life of Carbon-14 is 5,730 years, what is the value of the decay constant k to 5 decimal places?
-_____ k
_____ A0 = A0e
k ~= ______
Mathematics
1 answer:
Brrunno [24]3 years ago
5 0
In this scenario we know that carbon14 at a given time A(t) = A0e^(-kt), where A0 is the original carbon present, t is time in years and k is the constant.

As we are working with the half life of carbon being 5730 years, we assume original carbon-14 content, A0 = 1, and carbon-14 at half life 5730 years, A(t) = 0.5.

i.e. 
0.5 = 1e^(-5730k)
apply Ln to both sides of equation to cancel e
ln(0.5) = -5730k
k = ln(0.5) / -5730
k = -0.69315 / - 5730 = 1.20968 x 10^-4
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Answer:

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Step-by-step explanation:

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The simplification you are trying to do involves finding the prime factorization of a number. Since 125 is not divisible by 2, move on to 3. 125 is also not divisible by 3, so move on to 5. Then 125/5 = 25, and 25/5 = 5, so 125 = 5^3. The prime factorization of 125 is 5^3.

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