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) \(\frac { d x } { d t } = - 0.1 y , \frac { d y } { d t } = 0.5 x - 0.1 z , \frac { d z } { d t } = 0.5 y\)

Recognize the importance of environmental factors and community infrastructure in disease prevention.

Understand the historical development of public health initiatives and their impact on community health.

Analyze the role of government and non-governmental organizations in the advancement of public health.

Identify key figures and their contributions to public health and nursing.

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Definitions:

Agricultural Societies

Societies that rely on agriculture as their primary means for support and sustenance, cultivating plants and domesticating animals.

Food Production

The processes involved in the creation of food items, including agriculture, farming, and manufacturing.

Material Production

The process of creating goods and services through the combination of human labor, materials, and technology.

Psychodynamic Model

A view that explains personality in terms of conscious and unconscious forces, such as unconscious desires and beliefs.