112 EXAM V Section II Part A Free Response 2. A water tank holds 150 gallons of
ID: 2885056 • Letter: 1
Question
112 EXAM V Section II Part A Free Response 2. A water tank holds 150 gallons of water at time/-0. During the time interval OsiS 12, water is pumped into the tank at the rate of n(t)-4esinA) gallons per hour. At time -8 hours a second pump begins removing water from the tank at the rate of R(t)-?gallons per hour. 1+ (a) How many gallons of water enter the tank during the time interval 0sIs8 b) At what time during the time interval 0 Srs 8 hours is the amount of water increasing most rapidly? (c) What is the total amount of water in the tank at-12 hours? (d) Is the amount of water in the tank increasing or decreasing at r-12 hours? Justify your answerExplanation / Answer
Assuming this is from the AP,
we can use a calc for this...
w = rate of pumping in
r = rate of removing it out
a)
Just integrate w from 0 to 8,
we get 68.236 gallons-----> ANS
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b)
We gotta find w - R = 0
and then solve for t
We get t = 6 ---> ANS
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c)
We gotta do (integral of 0 to 12) w - R dt
and we get 27.324
27.324 + 150
177.324 gal ----> ANS
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d)
At t= 12, r is increasing but w is decreasing
So, clearly amt of water is DECREASING ----> ANS
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