- #1
eeriana
- 15
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Homework Statement
2 part question: part one is supposed to be a hint to part two.
1) find the general solution to the equation: dx/dt = x - x^2
2)A one gallon jug is half full of a liquid and half full of air. Additional liquid is being pumped in at a rate of 1/4 gallon per minute. If the rate at which the liquid flows into the container is proportional to both the volume of liquid in the jug and the volume of air in the jug, how long will it be before the jug is 90% full of liquid?
Homework Equations
dx/dt = r(i)c(i) - (r(o)/V)x
The Attempt at a Solution
If I have calculated the first part correctly, I came up with t = ln(x/1-x) - C
I know the rate in of the liquid is .25 gal/min. Rate out is 0. I am not seeing the connection to the first equation. If someone could point me in the right direction, I'd appreciate it.
Thanks