The rate of change of y with respect to t is proportional to 50 - y

We can write and solve the differential equation that fits the statement given;

dy/dt = k (50-t)

∫dy = ∫ k (50-t) dt

= ∫ (50k - kt) dt

therefore;

y = 50kt - k/2 (t²) + C

Alternatively, can be written as

y = - k/2 (50-t) ² + C)