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4. Radioactive Decay Series: Let r(t), y(t), and z(t) denote amounts of substances X, Y, and Z respectively, remaining at time t (X decays to Y and Y decays to Z where Z is the stable substance that we get at the end). A linear system of differential equations describing this dynamics can be written as da dt dy dt dz dt = -.12r .12r- .5y .5y (a) Explain the model in words (explain each differential equation then explain it as a system). (b) Solve for the amount of each substance if r(0) = xo (some initial quantity), y(0) = 0, and z(0) = 0.

4. Radioactive Decay Series: Let r(t), y(t), and z(t) denote amounts of substances X, Y, and Z respectively, remaining at time t (X decays to Y and Y decays to Z where Z is the stable substance that we get at the end). A linear system of differential equations describing this dynamics can be written as da dt dy dt dz dt = -.12r .12r- .5y .5y (a) Explain the model in words (explain each differential equation then explain it as a system). (b) Solve for the amount of each substance if r(0) = xo (some initial quantity), y(0) = 0, and z(0) = 0.

Advanced Engineering Mathematics
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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4. Radioactive Decay Series: Let r(t), y(t), and z(t) denote amounts of substances X, Y, and Z respectively, remaining at time t (X decays to Y and Y decays to Z where Z is the stable substance that we get at the end). A linear system of differential equations describing this dynamics can be written as da dt dy dt dz dt = -.12r .12r- .5y .5y (a) Explain the model in words (explain each differential equation then explain it as a system). (b) Solve for the amount of each substance if r(0) = xo (some initial quantity), y(0) = 0, and z(0) = 0.
Transcribed Image Text:4. Radioactive Decay Series: Let r(t), y(t), and z(t) denote amounts of substances X, Y, and Z respectively, remaining at time t (X decays to Y and Y decays to Z where Z is the stable substance that we get at the end). A linear system of differential equations describing this dynamics can be written as da dt dy dt dz dt = -.12r .12r- .5y .5y (a) Explain the model in words (explain each differential equation then explain it as a system). (b) Solve for the amount of each substance if r(0) = xo (some initial quantity), y(0) = 0, and z(0) = 0.
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