Communication Activitiy Results

Class: CalculusQuest Differential Calculus (OSU Section) - Authenticated as: robby (Administrator)

Communication Activity # 5001

Thread initiated by Dagwood at Step # 1

---Comments made by Dagwood at Exchange # 1---

QUESTION:

     Suppose that there is a water tank that is filled
 with 100 gallons of water and there is also a hole on the
 bottom of the tank that is allowing between 5 and 10
 gallons of water escape each minute.  Is it safe to
 assume that the tank will be empty in 10 to 20 minutes?



     If W(r) was the total amount of time it took to drain
 the water out of the tank for rate r, then we can assume
 that W is differentiable. 



W(5) =     (100 gallons)       = 20 minutes

	 (5 gallons/minute)



W(10) =      (100 gallons)     = 10 minutes

	   (10 gallons/minute)



Yes, it is safe to assume that the tank will be empty in
 10 to 20 minutes, since the water is always draining at a
 rate between 5 and 10 gallons per minute.

---Comments made by Blondie at Exchange # 2---

 Your writing style and usage of proper grammer were "done
 well", and all the information offered was pertenent to the
 subject at hand. If you go by the strict defenition of
 the MVT, then I dont think the issue this question raises
 at the end is quite pertnenant.  (i've discovered this
 after talking to a TA. so think i am contradicting
 myself, i assume i misinerpreted it also with the problem i
 chose)

The mean value therom says that there is some value c, on
 a continous function [a,b], where f'(c) = f(b)-f(a)/b-a.
 C is limited to one value, as opposed to a range of
 values as stated by the question (between ten and twenty
 minutes).  A different way to do the question might be to
 give the number of minutes it took to empty the tank and
 then use the ranges of numbers of gallons the tank will
 empty in a minute, and then try to figure out how many
 gallons per minute the tank was emptying at.  After you
 give that information you could say did the tank empty at
 some rate, such as, in at least 8 gallons per minute.  

As for the numbers, I felt they were realistic and
 illustrated good algebraic pratices.

---Comments made by Dagwood at Exchange # 3---

So, what you are saying is that I should change my
 question in such a way so I would give the number of
 minutes it took to empty the tank and also the range of
 gallons of water per minute that could have drained in that
 amount of time.  Then I should ask what was the volume of
 water that was emptied. That sounds pretty good, it would
 make the problem a little easier to understand and much
 easier to compute.  Thanks.



My newly revised question:

 Suppose that there is a water tank that is filled with
 100 gallons water and it takes between 50  and 60 minutes
 for it to drain completely.  If you let the tank drain
 completely, is it safe to say that the tank drained at a
 rate between 1.7 and 2.0 gallons per minute?

---Comments made by Blondie at Exchange # 4---

Yes, I feel those were appropriate changes to your
 problem. It now takes into account the fact that the
 function must be linear to describe the MVT. By using those
 two particular  sets of values the problem can be
 understood easily and is algebraicly easy to grasp.

---End Of Thread---

[Class Home] [Resources] [What's Next?]

QuestWriter 1.5