Please help, Growth and decay type question (1 Viewer)

[matt161989]

Hi, I am completely stuck. The question is "A vessel is being filled at a variable rate and the volume of liquid in the vessel at any time t is given by V=A(1-e to the power of -kt)" Question (a) was show that dV/dt = k(A-V) and i got that easily, however question (b) is "If one wuarter of the vessel is filled in 5 minutes, what fraction is filled in the next 5 minutes?"

Please help me I am completely stuffed and I have no idea,
Thanks in advance for any1 who can help, Matt

If you have the green "New Senior Mathematics, 3 unit course book," it's question 6 (b) in exercise 25 (e)

 

[rama_v]

http://community.boredofstudies.org...ariable+rate+the+volume+of+liquid+in+any+time

Again, if you have a difficult fitzpatrick question it has probably already been asked and solved
This is paticularly true of the projectile motion and simple harmonic motion questions.

 

[matt161989]

Thanks for that, though, it says V = A/4, if A is the initial volume then how how could one quarter of the vessel be 1/4 x A. e.g. if the initial volume is 2 litres then V = 1/2.

 

[insert-username]

When time is zero, V = 0 (V = A[1-e^-kt], when t=0, V = A x (1-1) = 0). In other words, the initial volume is zero, therefore the volume after 5 minutes is A/4 since we're starting from scratch.


I_F