1. No category

5.3 Slope Fields
AD
Related Rates
A spherical snowball melts in such
way that the instant at which its radius is 20cm , its
is decreasing at 3 cmlmin At What rate is the volume of the ball changing atthat
a
mains
instant
.
?
gun
r zoom
:
.
3
'
.
,
dart
:
tnfn
'
da¥
t
tom
•
Ean :
Viii
off z±*3r2
.
:
old
¥
-
Ktrdr
=
dt
At
t
)
cmt
4+120
:
:
3
ad
480 a
-
mhfn
min
h@ Slope tields
let's consider the following situation
Suppose
we
are
rate
Let
y
:
person learns
a
the percentage learned
Equation
Differential Equation
an
:
interested in how fast an employee learns
dif
=
.
a
given task
percentage of task not yet learned
=
time H
weeks)
y
=)
100
is such an equation
-
unknown function
:
by
at
-
.
that
.
.
an example of differential equation
gives information
.
about the rate of change of
Let's
say
rate holds
that work is a 5 day work week and let's assume 100% of the learning
for the first day How muh does the person need to learn in 1 day ?
.
day
:
:
We
Let's
can also
-
( 1 day
100g
100
-
120% )
:
=
Hsofwk)
80% per day
visualize differential equation using SLOPE FIELDS !
consider the differential equation :
days
:
Y
→
Any solution to the differential eqtn has the property
.
slope
of any
point is
equal to the y
-
coordinate
0
1
day
1
.
0
1
1
32
0
0
0
3
-
.
.
y
×
-
that the
3
-3
1
1
1
1
's Bes
Let 's
the differential equation :
dYq=2i
Sketch
.
field
slope
.
at
insider
-
-
-
-
-
-
¥txi2x
Y
X
-
the
1
2
2
4
4
-2
4
-4
-1
-1
-2
:2x
whose graph
passes
-
.
let's find the particular sodulimttke equation
¥
(1-2)
,
through
DI
dx
dy
Sdy
y
When Xl
=
4
y
2
Zxdx
:
=
-
:
y
:
2
x4c
HPTC
2=1
Kidx
x2+C
,
:
y
'
-
X2t1
to
1=c
←
ontidenvatie
.