Question

First order derivatives question

Answer 1

@hartnn

Answer 2

Perhaps I can help you get started:
Let s(t) = amount of salt in the serum-salt mixture at time t
Let (ds/dt) be the time rate of change in the amount of salt present in that mixture; it represents the NET rate of change (rate in, less rate out)

Let the volume of the serum-salt mixture be 0.5L+(3L/min)*t

Answer 3

\[\frac{ ds }{ dt }=(\frac{ 5L }{ \min })\frac{ 5gr }{ L}-(\frac{ 2L }{ \min })(\frac{ s }{ 0.5L+\frac{ 3L }{ \min} t})\]

Answer 4

Please take some time to go thru this equation. Ask any questions you want. I may not respond immediately, but will respond.

Answer 5

To answer this question, you'll need 2 pieces of information:
(1) the volume of the blood-salt mixture after 10 minutes (0.5L + 3(L/m)*10=?)
(2) the amount of salt in that mixture, in grams
Dividing the amt. of salt by the volume will give you the desired concentration of the salt remaining in the container.

Answer 6

If you'll look carefully at this equation, you'll see that every one of the 3 terms has the units of measurement grams per unit time (grams per minute). Dimensionally consistent!

Your job is to solve this d. e. for s as a function of time, t.