Math 391 Lecture 5 - Modeling with linear equations continued - Mixture Problems

In this lecture, we complete section 2.3 with one last application of first order linear ODEs--tank "mixture" problems. We discuss how to properly read the word problems associated with this topic, defined the important terms and figured out how to write down an ODE that modeled the situation. We then spent the remainder of the class going over three examples.

[kevinmarquez]

Jhevon, I transferred to the university at buffalo!! My current math professor sucks! And these videos are saving my life, thank you!!!!

[swanhtet]

Can you share the hand outs please? There is no link on your course site.

[sanelemaziya]

Have you done a water clock problem in any of your lectures? Great content by the way.

[Nooreazy]

You have saved my life. I dunno how I can thank you, I guess acing the test lol.

[aceandspace]

A 200 gallon tank contains 80 gallons of water in which is

dissolved 10 pounds of salt. Starting at time t = 0, fresh water is pumped into

the tank at a rate of 5 gallons per minute. At the same time, the well-stirred

mixture is pumped out at a the same rate.

Set up an initial value problem (differential equation and initial conditions)

whose solution is the amount Q(t) of salt (in pounds) in the tank at time t. You

need not solve the equation.

formulas as you stated: CinRin-(Q/Vo+(Rin-Rout))Rout

C in (10 lbs)
Rin-5 gallons
Q
Vo=80 gallons
(rin-rout) =0
t=0
R out =5

(10)(5)- (Q/(80+(5-5)) 5
Am i need the right track?

[erickrobles]

@jhevon Smith, in the differentials textbook, pg 56 to be exact, they say that K (for the money modeling differential equation) can be either positive (for deposits) or negative (for withdrawals). Should i stick with that idea? or should i go with the idea of "Rate in MINUS Rate out"? In your last video, the equation you provided was positive K. I want to avoid any confusion i am having. Thanks!

[ShwetankT]

the camera guy is like cos x, always behind sin x.

[UnforsakenXII]

It was a bit hard to figure out what each question was since there was no paper we could utilize to see the problem, lol. But it's free so I can't complain. Good Lecture.