(
>‘
4
h
cL>c
N
jTh
-o
(1
)<
J
‘c
-
-
>
-
I
.—
-
X
CU
+
?
-.
)
‘—
I
-
j
;
c:
0
-
I
t
+
r4+
3
‘
,ri
+
(1
—Th
ii
C.
L)
x
C
I’
rç
1
U
x
—
4
-
r’
(Th
I
‘
-1
—\
‘
4
3
C
c)
-4.
-à
,‘
+
.5
2
)
-
F-.
H-
4
‘
;3
L
3
.c-) c)
I
(—
LI
:4
x
C
J
C—)
LI
—
4>
,).
1
)&
-1_
-‘,,
d
—
(
-.
4
(-J
c——-Th
-
El
C’
(h1\
n
f-
)qc-)
cCLv
cTh
-r
11
I—’.
1)
‘1-
CXd
‘.
cC
()c
Cc
Error: 0 = e^{-1} +e^{-1}*C
C = -1
‘C
t
(_
ii
—
-I
-1-
‘—I
ji
0
11
-
1
0
v
-
I
>4
)
(
_)
)\
1
—
\
0
jl
÷
11
‘1
:5
I
p’J
p
p
,
n—.
iJ
-
4-1
ii
ii
-4-
:4=
I’
‘.1
\x—
Q
1
O14
-1’
•
A
I
Kr
-
-
uJ
K
()
‘—I
—t
1’
ii
NC
ii
II
J•
yy
U’
II
(
0
11
xfi
(
0
T
t
_
__
_
__
__
____
L:+h
\
tc
C
3o
\
0—
C5° oJo
5c+-.
C
A6/c: ‘1h’e.-€ js
mo(
ocb
-
50+t
V
cç
SL
c\J
.L
V
°
I
1L4
7r o
C
1
1
•
j
t)
C
c
5
occ
-f
j
F
Lso’--iY
A
—7
-t
2
S &
Goaôo
A
(...st°S’ ) .S’’
(‘)i?
-
g
‘“
_v_-’
—
•—
—
io-
‘-
,
1
cç
“..SLi
((s’1).js-)
‘11
).rC.S)
/
(0 ‘sr)
(oIo)
(s’l)ti
st)-(-i
st? (c’i-s’
0
0-
5’
-i 0
0
Q (oc,
-t)c
t
a
,“
I
7. A tank initially contains 50 gallons of brine, with 30 pounds of salt in solution. Water runs into the
tank at 3 gallons per minute and the well-stirred solutions run out at 2 gallons per minute. How long
will it be until there are 25 pounds of salt in the tank?
8. Use Euler’s Method with h
=
.25 to approximate the solution over the indicated interval
y(0)=0,
,
2
y’=x
XE[0.11
9. Find the solution to the differential equation
dy
=ay+b.
10. Below is the slope field for the logistic growth model for a population y is
=
ky (L
-
y)
Where t represent time, L = 100, represents the carrying capacity, k
Sketch the solution on the slope field for y, given y(0) = 25.
211(1
I
I
150
(10
,
,.
,
//// /7///1////////
II! !!/I//II/IfI/II
11 1I1///!I11//lulI
50
‘1//If//If f/f//Ill /
/ / / / / / / / / / / / / / / / /1 /
///////////////////
0
(L2
0.4
What is
(a)
L/2?
y, if y(0)
(b) lirny,ify(0)=0?
(c) lirn y, if y(0)
=
Q
2L?
—
06
0.8
I
=
.2, represents the growth rate.