Question

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

Answer 1

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)