CALCULUS HELPPPP

Question

A storage tank at a factory collects liquid waste and can be drained by opening a drainage valve at the
base of the tank. The depth, d(t), of fluid in the tank t hours after the valve is opened is given by the
formula below.

d(t)=6(1-t/12)² meters

 

 

a. Daily production in the factory ends at 5:30 p.m. If the valve is opened at 6:30 p.m. and remains
open, at what time will the tank be completely empty? Explain how you arrived at your answer.

 

b. At 10:30 a.m., the storage tank is completely full and the valve is left open until 1:45 p.m. How many
meters of liquid waste have emptied from the tank by 1:45 p.m.?

 

c. What is the value of
d'(2)
. Using correct units of measure, explain what this value represents.

 

d. Is waste draining faster after 30 minutes or after 2 hours? Justify your answer

 

Answer 1

a.  derive it.

 

12(1-t/12)(-1/12= -(1-t/12).  

 

So derivative is -(1-t/12) or -1+t/12 if you distribute the - sign. You can use either. 

 

Set this equal to 0

0=-1+t/12

 

t=12. 

 

Time for it to drain is 12 hours. 

 

Part b.  You should just be able to plug in 3.25 hours into the derivative and see what the change is with respect to time. 

 

So -1+3.25/12=-.729meters

 

Part C plug into derivative.  That should represent the change in the depth in 2 hours.

 

Part D.  Plug both into derivative and see change in depth.  Waste is draining faster at 30 minutes which is .5 hours than 2 hours.