A tank holds 70 gallons of water, which drains from a leak at the bottem, causin

Question

A tank holds 70 gallons of water, which drains from a leak at the bottem, causing the tank to empty in 36 minutes. The tank drains faster wihen it is nearty ful because the pressure on the leak is greater . Toricellr·Law gives the volumn of water remaining in the tank after t minutes (a) Find vO) and V36). gal gal 36) (b) What do your answers to part (a) represent? 36) represents the initial volume, and 0) represents the final voume. O) represents the initial volume, and VI36) represents the final volume (e) Make a table of values of Vic) for t 0,9,18, 27, 36. t Cin minutes) vtn Cin eallons) 18

Explanation / Answer

v(t)=70(1-t/36)2

a. V(0)=70(1-0/36)2= 70(1)=70

V(36)= 70(1-36/36)2= 70(1-1)2=0

At time t= 0 means the initial value , therefore the correct option is the second option

t V(t) 0 70 9 39.375 18 17.5 27 4.375 36 0

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