Radioactive Element X Decays to Element Y with Decay Constant $- 0.5$

question 14

Multiple Choice

Radioactive element X decays to element Y with decay constant $- 0.5$ . Y, in turn, decays to stable element Z with decay constant $- 0.1$ . 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, if the initial conditions are $x ( 0 ) = 10 , y ( 0 ) = 0 , z ( 0 ) = 0$ .

• A) \(\frac { d x } { d t } = - 0.5 x , \frac { d y } { d t } = 0.1 x - 0.5 y , \frac { d z } { d t } = 0.2 y\)
• B) \(\frac { d x } { d t } = - 0.5 x , \frac { d y } { d t } = 0.5 x - 0.1 y , \frac { d z } { d t } = 0.5 y\)
• C) \(\frac { d x } { d t } = - 0.5 x , \frac { d y } { d t } = 0.5 x - 0.1 y , \frac { d z } { d t } = 0.1 y\)
• D) \(\frac { d x } { d t } = - 0.1 x , \frac { d y } { d t } = 0.1 x - 0.5 y , \frac { d z } { d t } = 0.1 y\)
• E) \(\frac { d x } { d t } = - 0.1 y , \frac { d y } { d t } = 0.5 x - 0.1 z , \frac { d z } { d t } = 0.5 y\)

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Definitions:

Conveys

Transfers ownership or title of property or rights from one person or entity to another.

Nonpossessory Interest

In the context of real property, an interest that involves the right to use land but not the right to possess it.

Easement

A right granted to use another's property for a specific purpose, such as right of way or utility installation.

Possess

To have or hold property, assets, or rights, either legally or physically.