Radioactive Element X Decays to Element Y with Decay Constant $- 0.2$

question 40

Multiple Choice

Radioactive element X decays to element Y with decay constant -0.3. Y decays to stable element Z with decay constant $- 0.2$ . What is the system of differential equations for the amounts, $x ( t ) , y ( t ) , z ( t )$ of the elements X, Y, Z, respectively, at time t.

• A) \(\frac { d x } { d t } = - 0.2 x , \frac { d y } { d t } = 0.2 x - 0.3 y , \frac { d z } { d t } = 0.2 y\)
• B) \(\frac { d x } { d t } = - 0.2 x , \frac { d y } { d t } = 0.2 x - 0.3 y , \frac { d z } { d t } = 0.3 y\)
• C) \(\frac { d x } { d t } = - 0.3 x , \frac { d y } { d t } = 0.3 x - 0.2 y , \frac { d z } { d t } = 0.2 y\)
• D) \(\frac { d x } { d t } = - 0.3 x , \frac { d y } { d t } = 0.3 x - 0.2 y , \frac { d z } { d t } = 0.3 y\)
• E) \(\frac { d x } { d t } = - 0.3 y , \frac { d y } { d t } = 0.3 x - 0.2 y , \frac { d z } { d t } = 0.2 y\)

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