Question

i.) set up the differential equation that models the problem;

ii.) solve the equation and write up details of the solution;

iii.) use it answer the questions asked;

iv.) write a software program that sketches a graph of the solution;

v.) determine the limiting behavior of the modeled system.

Problem 3. Two aquariums each contain 100 gal of water with 3 gm of an impurity. The tanks are connected in sequence; clean water flows into the first tank at a rate of 5 gal/min, the well mixed mixture flows into the second tank at the same rate and the second tank drains out its well mixed mixture at the same rate. Find the equations hat models the impurity in the two tanks. For each tank, determine how long it takes the level of impurity to decrease toof its original level; determine how long it takes the level of impurity to decrease to of its original level

Answer 1

) |unu/s 33 m Sgol/i ogod sgal/min Cmount o Saut in tankI, tankI. wB u! min in Saut out] = [Saut In clt 5 X Lo)39m. 20 ISaut InJ-IsS at out] clt R! 3gm 5x 2.O (+),R 2 o 2 o (+7 A

スー=」ス - Y =1 x Lt) = Ce 2o =) (0): 3=c. LE 3e-t/20 ) 3e-20 20 e to e 20 deto P ニ 3 20 (47A e20 3 t e- t/20 20 Ze-20 3E p-20 20 て= 3. 2 0 3te-/20 gm 3e-20 2o tこt」 =) cut min 3 e-20 = 3 -) t, = ) 20lnl2) | 13.863min Hat t= t2 ) Lt2) =3 at E 3e-20 36e-/20 2o ) e 2o = 33. S669 min t, = 20 2 ヒ=ヒ3 =) xlt3)=1. =)と3=)20L7 (3) t 21.972min at Gnu ird ty =) l ty)= ) cut t= ) ty = |4 S. 78S6 mın

-3.5 2.9 -2 -1.5 1 0.5 90 400 R0 70 50 40 30 20 10 -

v Amount Cl Seų Lam) 3 (7) A Cmin) 3 e-t120 lim v) (+7 3e-203 te- Lt= Lim co 20 2O Lim 20ett/20 33 e 2o co uning hopita Rule