{Use of Tech} Flow from a tank A cylindrical tank ​​is full at time t=0 when a valve in the bottom of the tank is opened. By Torricelli’s law, the volume of water in the tank after t hours is V=100(200−t)², measured in cubic meters.
c. Find the rate at which water flows from the tank and plot the flow rate function. 

Verified step by step guidance

1. Step 1: Understand the problem. We need to find the rate at which water flows from the tank. This is the derivative of the volume function V with respect to time t, which gives us the flow rate function.
2. Step 2: Identify the volume function. The volume of water in the tank at time t is given by V(t) = 100(200 - t)^2.
3. Step 3: Differentiate the volume function with respect to time t. Use the chain rule to find the derivative of V(t). The chain rule states that if you have a composite function, the derivative is the derivative of the outer function evaluated at the inner function times the derivative of the inner function.
4. Step 4: Apply the chain rule. Let u = 200 - t, then V(t) = 100u^2. The derivative of V with respect to u is 200u, and the derivative of u with respect to t is -1. Therefore, the derivative of V with respect to t is dV/dt = 200u * (-1).
5. Step 5: Substitute back the expression for u. Since u = 200 - t, substitute this back into the derivative to get the flow rate function: dV/dt = -200(200 - t). This function represents the rate at which water flows from the tank.