1 Attachment(s)
Differential Equations Calculation Question
Liquid is pouring into a container at a constant rate of 20 cm 3s-1 and is leaking out at a rate proportional to the volume of the liquid already in the container.
(a) explain why, at time t seconds, the volume, V cm3 of liquid in the container satisfies the differential equation dv / dt = 20 - kV, where k is a positive constant.
The container is initially empty.
(b) by solving the differential equation, show that V= A + Be-kt, giving the values of A and B in terms of k.
So given that dv / dt = 10 when t = 5
(c) find the volume of liquid in the container at 10s after the start.
(p.s.i have attached a document with my own answers)
Re: Differential Equations Calculation Question
Quote:
Originally Posted by
huntelaar2011 
Liquid is pouring into a container at a constant rate of 20 cm 3s-1 and is leaking out at a rate proportional to the volume of the liquid already in the container.
(a) explain why, at time t seconds, the volume, V cm3 of liquid in the container satisfies the differential equation dv / dt = 20 - kV, where k is a positive constant.
The container is initially empty.
(b) by solving the differential equation, show that V= A + Be-kt, giving the values of A and B in terms of k.
So given that dv / dt = 10 when t = 5
(c) find the volume of liquid in the container at 10s after the start.
(p.s. i do have my own answers but wanted to see if a different calculation is given by others, i can post my answers up on this thread if others want to see my own work).
Please post all your work and answers so that it can be critically reviewed. People do not have time to waste repeating what may turn out to be what you've already done.
