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 minutes. At the same time

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Question 1146036: 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 minutes. 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) = 15t2 gallons per minute, where t is in minutes.
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 tank and the volume of water leaking out of the tank. Find the volume function, V(t).
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


The statement of the problem is incorrect.

The difference between the two functions showing how fast water is being pumped in and how fast it is leaking out only tell you how the volume is changing as a function of time; it does NOT give you the volume as a function of time.

So the function showing how the volume of water is changing ("C(t)") is



Then the VOLUME function V(t) is the initial volume V(0) plus C(t).

ANSWER:
The volume function is
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.

            To the author of this problem / post.

            There is a FATAL discrepancy / inconsistency in terminology you use. 


When you describe function P(t), you give its dimension unit as "gallons per minute".


Such a function is (has the technical name) "rate of inflow".

But if it is "rate of inflow", it is NOT the volume of the water in the tank.



The same thing is with the function L(t).



When you describe the function L(t), you give its dimension unit as "gallons per minute".


Such a function is (has the technical name) "rate of emptying", or "rate of drainage", or "rate of outflow".

But if it is "rate of emptying", it is NOT the volume of the water in the tank.



Using correct terminology is a MUST when you formulate a problem.


Therefore, there is no any sense in solving the problem as it is presented in the post, until it is fixed.


Make all necessary corrections, and then re-post the problem to the forum.


Do not post it to me personally.


------------

By the way, when you re-think the problem to the end, you may find that it EITHER has no sense at all,

OR has totally different meaning than you thought before.


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