Question

You may only ask the following question about this problem: "Is there an error on this problem?" SHOW ALL NECESSARY WORK including algebra, calculus, graphing, trig, etc... Put a box around your final answer Do Not Approximate Explain your reasoning where necessary A 500 liter tank of salt water contains 2 gram/liter of salt. Salt water containing 8 gm L of salt enters the tank at 10 liter minute while fluid exits the well mixed solution also at 10 L/min Write a fully simplified equation for the amount of salt in the tank at any time.

Answer 1

Given, gnitial amount of salt 2gM/L X500L = 1000gm = y(o) = 1000 Let ylt) denote the teoric amount of salt in the tank at any time (in minute Rate of change of amount of salt dy at = Rate of amount of salt entering (R) -Rate of amount o of salt leaving (R2) dy = Rp - R2 Now, R2 = 8gm/L X 10 L/minutes 80gm/minutes R₂ = y gm/L X 10 L/minutes soo tot °o101-101=0 no litre of water. added

dy dt 80 - y_X10 500 U dy = 80-y dt 50

CIASSMAte Date Page dy + y = 80 dt 50 gt is Linear first order D.E I dt 4/50 - I. F e t150)(80) dt elso 9 (4)%e8150) = slet 7 (4) (et so tiso tiso 80X50) e + c y = 4000 + ce y (0) - 4000 + 6 = 1000 ley 6=-3000 Fully simplified equation of the amount of salt in the tank at any time (in minutes) -t/so = y(t) = 4000 -3.000 e