Remains have been found containing 8 % of the original amount of Carbon-14. Recall that the Carbon-14 half-life is T = 5730 years. (a) Find the Carbon-14 decay constant, that is, the positive number r such that N' = -r N, where N is the amount of Carbon-14 in a dead organism as function of time, t, with t = 0 at the time the organism died. r = Σ (b) Date the remains, that is, find the number tị, the number of years since the organism died. ti = Σ

Remains have been found containing 8 % of the original amount of Carbon-14. Recall that the Carbon-14 half-life is T = 5730 years. (a) Find the Carbon-14 decay constant, that is, the positive number r such that N' = -r N, where N is the amount of Carbon-14 in a dead organism as function of time, t, with t = 0 at the time the organism died. r = Σ (b) Date the remains, that is, find the number tị, the number of years since the organism died. ti = Σ

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Remains have been found containing 8 % of the original amount of Carbon-14. Recall that the Carbon-14 half-life is T = 5730 years.
(a) Find the Carbon-14 decay constant, that is, the positive number r such that N' = -r N, where N is the amount of Carbon-14 in a dead organism as
function of time, t, with t = 0 at the time the organism died.
r =
Σ
(b) Date the remains, that is, find the number tị, the number of years since the organism died.
ti =
Σ

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