1
MATH 141B
Quiz#7
Due: Tues March 18, 2008
More interesting and realistic models take some time to set up. However, since I’ve clearly
laid things out, you’ll simply be going through the 7step method to solve a linear differential
equation, and taking a limit to get long range information.
[ 2 ]
1.
A 100gallon is filled with
pure water
. Salt water (brine) of concentration 0.1 pounds of salt
per gallon of water is pumped into the tank at 25 gallons per minute. Brine leaves the tank
at the same rate. Let
y
(
t
) denote the amount of salt in the tank at time
t
. Set up and solve
a first order differential equation for the unknown function
y
(
t
) and compute the amount of
salt in the tank in the long run. That is, find
y
∞
= lim
t
→∞
y
(
t
)
.
In this problem, you will be using the differential equation
y
′
=

(
F
V
)
y
+
I.
Note that
I
=
c
·
F
, as the units confirm:
lbs
gal
·
gal
min
=
lbs
min
(since gallons cancel).
A)
y
∞
= 10,
B)
y
∞
= 15,
C)
y
∞
= 20,
D)
y
∞
= 25,
E) none of the above
[ 2 ]
2.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 MARCFABBRI
 Math, Logic, Radioactive Decay, Lake Erie

Click to edit the document details