write an expression for the rate at which the water is changing in the tank

Question

water is pumped into an underground tank at a constant rate of 8 gallons per minute. water leaks out of the tank at the rate of √t+1 gallons per minute, for 0≤t≤120 minutes. At time t=0, the tank contains 30 gallons of water.

Answer 1

Let x = x(t) is volume of water in tank at time t. Then rate dx/dt = 8 - √t - 1; dx/dt = 7 - √t;

x(t) = 7t - 2/3t^3/2 + C; x(0) = C = 30. x(t) = 7t - 2/3t^3/2 + 30