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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