Volume Q (1 Viewer)

[TrueHappiness]

A vessel filled with liquid is being emptied and the volume V cubic metres remainng after t minutes is given by V = Ae^-kt

a)Show that dV/dt = -kV
B) If one quater of the vessel is emptied in the first 5 minutes, what fraction remains after 10 minutes
c) At what rate is the liquid flowing out
i) After 10minutes
ii) When one quarter of the vessel is empty.

I do not get b at all. IS no numerals are given, how are we meant to do it?

 

[bachviete]

A vessel filled with liquid is being emptied and the volume V cubic metres remainng after t minutes is given by V = Ae^-kt

a)Show that dV/dt = -kV
B) If one quater of the vessel is emptied in the first 5 minutes, what fraction remains after 10 minutes
c) At what rate is the liquid flowing out
i) After 10minutes
ii) When one quarter of the vessel is empty.

I do not get b at all. IS no numerals are given, how are we meant to do it?

Recall that the initial quantity is "A", ie V = A

So When its three quarters full, V = 3/4 V.

.: 3/4 V = V e^-5k

.: 3/4 = e^-5k

Then just solve via logs for k