Radioactive Decay of Carbon-14 (¹4C) The half-life of ¹4C is 5730 years (yr). If the original amount of ¹4C in a particular living organism is 20 grams (g) and found in a fossil of that organism 0.01 g, determine the approximate age of the fossil. Evaluate the remaining amount of ¹4C after 90,000 yr. Hints: Let m(t) represent amount of 14C at time t. We have the initial amount m(0) = 20 g. The half-life time is T = 5730 yr. a piece of information The 14C found in the fossil at an unknown time t* is m(t*) = 0.01 g We want to evaluate the approximate age of the fossil, i.e., we need to find the time t* at which the amount of ¹4C dropped from 20 g to 0.01 g. • The IVP that represents the decay model is dm m(0) = 20. dt (i) Solve the IVP, (ii) find k, (iii) the age of the fossil t and (iv) evaluate m(90000). = km,
Radioactive Decay of Carbon-14 (¹4C) The half-life of ¹4C is 5730 years (yr). If the original amount of ¹4C in a particular living organism is 20 grams (g) and found in a fossil of that organism 0.01 g, determine the approximate age of the fossil. Evaluate the remaining amount of ¹4C after 90,000 yr. Hints: Let m(t) represent amount of 14C at time t. We have the initial amount m(0) = 20 g. The half-life time is T = 5730 yr. a piece of information The 14C found in the fossil at an unknown time t* is m(t*) = 0.01 g We want to evaluate the approximate age of the fossil, i.e., we need to find the time t* at which the amount of ¹4C dropped from 20 g to 0.01 g. • The IVP that represents the decay model is dm m(0) = 20. dt (i) Solve the IVP, (ii) find k, (iii) the age of the fossil t and (iv) evaluate m(90000). = km,
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 14EQ
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Transcribed Image Text:4. Radioactive Decay of Carbon-14 (¹4C)
The half-life of ¹4C is 5730 years (yr). If the original amount of ¹4C in a particular living organism
is 20 grams (g) and found in a fossil of that organism 0.01 g, determine the approximate age of
the fossil. Evaluate the remaining amount of ¹4C after 90,000 yr.
Hints:
Let m(t) represent amount of 14C at time t.
We have the initial amount m(0)
20 g.
The half-life time is T = - 5730 yr.
a piece of information
The 14C found in the fossil at an unknown time t* is m(t*) = 0.01 g
We want to evaluate the approximate age of the fossil, i.e., we need to find the time t* at which
the amount of ¹4C dropped from 20 g to 0.01 g.
• The IVP that represents the decay model is
dm
dt
m(0) = 20.
(i) Solve the IVP, (ii) find k, (iii) the age of the fossil t and (iv) evaluate m(90000).
= km,
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