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

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) $\frac { d Y } { d s } = k ( 50 - s ) ^ { 2 } , Y = - \frac { k } { 3 } ( 50 - s ) ^ { 3 } + C$