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HELP - more differentiation

Liquid is poured into a container at a constant rate of 20cmcubed per second. after t seconds liquid is leaking from the container at a rate of v/10 cmcubed per second, where v cmcubed is the volume of liquid in the container at that time.

Show that -10 dv/dt = v - 200
given that v =500 when t = 0

b) find a solution of the differential equation in the form v = f (t)

Find the limiting value of v as t tends to infinity
Reply 1
Avatar for Aired
Aired
1
-dv/dt = (v/10) - 20
-10 dv/dt = 10(v/10 - 20)
-10 dv/dt = v - 200
Reply 2
Avatar for Chewwy
Chewwy
17
dv/dt = 20 - v/10

times by -10

-10/(v-200) dv = 1 dt

integrate to get...

-10ln(v-200) = t + c

(500,0)

-10ln(300) = c

so -10ln(v-200) = t - 10ln(300)

10ln(300/(v-200)) = t

e^t = (300/(v-200))^10

e^t/10 = 300/(v-200)

v = 300/e^t/10 + 200

as t gets big, e^t/10 gets big, so 300 over it gets small, so in the limit v = 200. bet everything i post is wrong, so check my working.

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