Question

Calculus help?

Answer 1

When air is released from an inflated balloon it is found that the rate of decrease of the volume of the balloon is proportional to the volume of the balloon. This can be represented by the differential equation,\[\frac{dv}{dt}=-kv\],where v is the volume, t is the time and k is the constant of proportionality.

If the initial volume of the balloon is v_0, find an expression, in terms of k, for the volume of the balloon at time t.

Answer 2

how is this a related rates problem?

Answer 3

this is just diff eq problem... separate the variables then integrate...

Answer 4

Is it not? Well, then what's the v_0 for then if I just integrate?

Answer 5

Now I have lnv = -kt + c
Is c = v_0?

Answer 6

My final answer is\[v=e^{-k+v_0}\]Is this correct?

Answer 7

yep.

Answer 8

Oh, I got it! Ok thanks :)

Answer 9

wait... what happened to the t?

Answer 10

Oh, yeah I meant\[e^{-kt+v_0}\]lol

Answer 11

better.

Answer 12

:D