The volume of water remaining in a hot tub when it is being drained satisfies the differential equation dV/dt = −3(V)^1/2 , wher
e V is the number of cubic feet of water that remain t minutes after the drain is opened. Find V if the tub initially contained 225 cubic feet of water.
The given function is a variable separable differential equation. Combine like terms, integrate, apply the appropriate limits, and express V in terms of t. This is done as follows:
dV/dt = -3(V)^1/2 dV/-3V^1/2 = dt
m here is the initial V which is 225. Then after integrating,
-2/3 (√V - √225) = t -2/3 (√V - 15) = t
That is the expression for V at time t. I hope I was able to help. Have a good day.