SOLUTION: At A water tank is being filled by water being pumped into the tank at a volume given by the formula P(t)= 112t+2000 gallons per minute, where t is in minute. At the same time the

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Question 1165685: At A water tank is being filled by water being pumped into the tank at a volume given by the formula P(t)= 112t+2000 gallons per minute, where t is in minute. At the same time the water tank has a leak and the volume of water draining out of the tank is given by the formula L(t)=15t^2 gallons per minute, where t is in mintues.
a. The volume V of water in the tank at any minute, t, is the difference of the volume of the water being pumped into the volume of water leaking out of the tank. Find the volume function, V(t).

Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.

The problem explains you in all details that the net inflow is the difference of the inflow and outflow
(the fact which is OBVIOUS even without explanations). 


    Therefore, all you need is to subtract the function describing outflow from the function describing inflow


        V(t) = P(T) - L(t) = 112t + 200 - 15t^2   gallons,


    or, which is the same, but ordered differently,


        V(t) = -15t^2 + 112t + 200   gallons.


Solved and explained in all details.



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