SOLUTION: 3. Initially a tank contains 10,000 liters of liquid. At the time t=0 minutes a tap is opened, and liquid then flows out of the tank. The volume of liquid, V liters, which remains

Question 1102754: 3. Initially a tank contains 10,000 liters of liquid. At the time t=0 minutes a tap is opened, and liquid then flows out of the tank. The volume of liquid, V liters, which remains in the tank after t minutes is given by V=10,000(0.933)^t.
a. Find out how much liquid is in the tank after 5 minutes.
b. Find out how long, to the nearest second, it takes for half of the initial amount of liquid to flow out of the tank.
c. The tank is regarded as effectively empty when 95% of the liquid has flowed out. Show that this takes almost three-quarters of an hour.
d. (i) Find the value of 10,000 - V when t=0.001 minutes.
(ii) Hence, or otherwise, estimate the initial flow rate of the liquid.
Give your answer in liters per minute, correct to two significant figures.

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
3. Initially a tank contains 10,000 liters of liquid. At the time t=0 minutes a tap is opened, and liquid then flows out of the tank. The volume of liquid, V liters, which remains in the tank after t minutes is given by V=10,000(0.933)^t.
a. Find out how much liquid is in the tank after 5 minutes.
Sub 5 for t, calculate.
=======================
b. Find out how long, to the nearest second, it takes for half of the initial amount of liquid to flow out of the tank.
V=10,000(0.933)^t = 5000
Solve for t.
========================
c. The tank is regarded as effectively empty when 95% of the liquid has flowed out. Show that this takes almost three-quarters of an hour.
V=10,000(0.933)^t = 500
Solve for t.
========================
d. (i) Find the value of 10,000 - V when t=0.001 minutes
Sub 0.001 for t.
====================
(ii) Hence, or otherwise, estimate the initial flow rate of the liquid.
Give your answer in liters per minute, correct to two significant figures.
The result of d. (i) above is a good estimate.

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