Write and Solve the Differential Equation That Models the Following $Y$

question 41

Multiple Choice

Write and solve the differential equation that models the following verbal statement: The rate of change of $Y$ with respect to $s$ is proportional to
$50 - s$ .

• A) \(\frac { d Y } { d s } = k ( 50 - s ) ^ { - 1 } , Y = - k \ln ( 50 - s ) ^ { 2 } + C\)
• B) \(\frac { d Y } { d s } = k ( 50 - s ) ^ { - 1 } , Y = - k ( 50 - s ) + C\)
• C) \(\frac { d Y } { d s } = k ( 50 - s ) , Y = - \frac { k } { 2 } ( 50 - s ) ^ { 2 } + C\)
• D) \(\frac { d Y } { d s } = k ( 50 - s ) ^ { 3 } , Y = - \frac { k } { 4 } ( 50 - s ) ^ { 4 } + C\)
• E) \(\frac { d Y } { d s } = k ( 50 - s ) ^ { 2 } , Y = - \frac { k } { 3 } ( 50 - s ) ^ { 3 } + C\)

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Definitions:

Promotions

The advancement of an employee's rank or position in an organizational hierarchy system.

Psychological Withdrawal

An employee's disengagement and lack of psychological presence at work, often manifesting as daydreaming, socializing, or looking for other jobs during work hours.

Organizational Commitment

The degree to which an employee identifies with the organization and is willing to put forth effort on its behalf.

Psychological Job Withdrawal

A process by which employees detach from their work roles, often manifesting through reduced engagement, effort, and commitment.