Question

A tank that holds 4000 gallons of water will drain completely into a reservoir in 32 minutes. The volume of remaining water in tank after time t is given by the function:

V(t)=4000(1-t/32)^2, 0<t<32

The amount of water in reservoir depends on how much water has drained out of the tank and defined by A(V)= 14000-V. After how many minutes will the amount of water in the reservoir reach 12000 gallons?

Answer 1

well, it looks like you want

A(V) = 12000
14000-4000(1-t/32)^2 = 12000
4000(1-t/32)^2 = 2000
(1-t/32)^2 = 1/2
1 - t/32 = ±1/√2
t/32 = 1±1/√2
t = 32(1±1/√2)
Since the domain of V is t<32, we need
t = 32(1-1/√2) = 9.37