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Help with solving a algebra word problem

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An artifact was found and tested for its carbon-14 content.  If 87% of the original carbon-14 was still present, what is probable age (to the nearest 100 years?) (Carbon-14 has a half-life of 5,730 years.)

Nov 24th, 2014

using the half life formula.
A(t) = Ao(1/2)^(t/Th)

Here, A(t) = Carbon content at time t. = 0.87Ao
Ao= Initial carbon content
Th= Half life
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0.87*Ao = Ao(1/2)^(t/5730)
---
(1/2)^(t/5730) = 0.87
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Take the log:

---
(t/5730) = log(0.87)/log(1/2) = 0.20091
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t = 5730*0.20091 = 1151.21 years, or 1200 years (nearest hundred)

Please best my answer if helpful. Thanks :)

Nov 24th, 2014

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