Problema Solution
carbon-14 has a half life of 5730 years.
a. write a decay function for a 12 mg. sample
b. find the amount of carbon-14 remaining after 2500 years (round to nearest tenth)
Answer provided by our tutors
a. write a decay function for a 12 mg. sample
Original amount (at time zero)
A(0) = 12 mg
Amount at "half-life" time
A(5730) = (1/2) * 12 mg = 6 mg (the definition of half-life)
An exponential decay function is of the form
A(t) = A(0) * e^(-kt), where k is a constant that we need to find
A(5730) = A(0) * e^(-k5730)
6 = 12 * e^(-k(5730)
.5 = e^(-k(5730)
ln(.5) = -5730k
k = 0.00012097
A(t) = 12 * e^((-0.00012097)t)
b. find the amount of carbon-14 remaining after 2500 years (round to nearest tenth)
A(2500) = 12 * e^((-0.00012097)*2500)
e = 2.7183
A(2500) = 12 * 2.7183^((-0.00012097)*2500)
A(2500) = 8.87 mg
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