FS10_1825_006_Sept27_notes

FS10_1825_006_Sept27_notes - MTH
1825
sec.
006
 


Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MTH
1825
sec.
006
 
 Monday,
Sept.
27,
2010
 Section
2.4
–
Applications
of
Linear
Equations
and
Modeling
 
 Example
1:

(Similar
to
#7‐10
in
section
2.4)
 
 Rachel
is
a
sales
representative
and
earns
a
base
salary
of
$2000
per
month
plus
a
12%
 commission
on
her
sales
for
the
month.
 
 a.
 Write
a
linear
equation
that
expresses
Rachel’s
monthly
salary
y
in
terms
of
her
 monthly
sales
x.
 
 
 
 b.
 Graph
the
equation.
 
 
 
 
 
 
 
 
 
 
 
 
 c.
 What
is
the
y‐intercept
and
what
does
it
represent
in
the
context
of
this
problem?
 
 
 
 
 
 d.
 What
is
the
slope
of
the
line
and
what
does
it
represent
in
the
context
of
this
problem?
 
 
 
 
 
 e.
 How
much
will
Rachel
make
(for
the
month)
if
her
sales
for
the
month
are
$25,000?
 
 
 
 
 f.
 If
Rachel
wants
to
make
$4500
in
a
month,
what
do
her
sales
have
to
be
for
the
month?
 
 
 
 Page
1
of
5
 MTH
1825
sec.
006
 
 Monday,
Sept.
27,
2010
 Example
2:

(#14
in
section
2.4)
 
 Let
y
represent
the
average
number
of
miles
driven
per
year
for
passenger
cars
in
the
 United
States
since
1980.

Let
x
represent
the
year
where
x=0
corresponds
to
1980,
x=1
 corresponds
to
1981,
etc.

The
average
yearly
mileage
for
passenger
cars
can
be
 approximated
by
the
equation
 y = 142 x + 9060 ,
where
 x ≥ 0 .
 
 
 a.
 Use
the
linear
equation
to
approximate
the
average
yearly
mileage
for
passenger
cars
 € € in
the
United
States
in
the
year
2005.
 
 
 
 
 
 
 b.
 Use
the
linear
equation
to
approximate
the
average
yearly
mileage
for
the
year
1985,
 and
compare
it
with
the
actual
value
of
9770
miles.
 
 
 
 
 
 
 c.
 What
is
the
slope
of
the
line
and
what
does
it
mean
in
the
context
of
this
problem?
 
 
 
 
 
 
 
 d.
 What
is
the
y‐intercept
and
what
does
it
mean
in
the
context
of
this
problem?
 
 
 
 
 
 
 
 During
what
year
does
the
equation
predict
the
average
yearly
mileage
will
be
13,300
 miles?
 
 
 
 Page
2
of
5
 MTH
1825
sec.
006
 
 Monday,
Sept.
27,
2010
 Example
3:

(#16
in
section
2.4)
 
 The
figure
represents
the
winning
time
for
the
men’s
100‐m
freestyle
swimming
event
for
 selected
Olympic
games.
 
 
 
 
 
 
 
 
 
 
 
 a.
 Let
y
represent
the
winning
time
(in
seconds).

Let
x
represent
the
number
of
years
 since
1948.

Use
the
ordered
pairs
given
in
the
graph
to
find
a
linear
equation
to
 estimate
the
winning
time
for
the
men’s
100‐m
freestyle
versus
the
year.

Round
the
 slope
to
2
decimal
places.
 
 
 
 
 
 
 
 b.
 Use
the
linear
equation
from
part
(a)

to
approximate
the
winning
100‐m
time
for
the
 year
1972,
and
compare
it
with
the
actual
winning
time
of
51.2
sec.
 
 
 
 
 c.
 Use
the
linear
equation
to
approximate
the
winning
time
for
the
year
1988.
 
 
 
 
 d.
 What
is
the
slope
of
the
line
and
what
does
it
mean
in
the
context
of
this
problem?
 
 
 
 
 e.
 Interpret
the
meaning
of
the
x‐intercept
of
this
line
in
the
context
of
this
problem.
 
 
 Page
3
of
5
 MTH
1825
sec.
006
 
 Monday,
Sept.
27,
2010
 Section
2.5
–
Introduction
to
Relations
 
 A
relation
in
x
and
y
is:
 
 
 The
domain
of
a
relation
is:
 
 The
range
of
a
relation
is:
 
 
 Relations
are
expressed
in
multiple
ways
in
your
textbook:
 
 1.
 
 
 
 
 
 
 
 
 
 
 
 2.
 
 
 3.
 
 
 
 
 
 
 
 
 
 
 
 4.
 
 
 
 Example
1:

Find
the
domain
and
range
of
the
relation
 {( 3, − 5), (6, 0), (−1, 8), (6, 2)} .
 
 
 Domain:
 
 
 
 
 
 
 
 Range:
 
 € 
 
 Example
2:

The
following
table
represents
the
number
of
students
enrolled
in
MTH
1825
 at
the
end
of
certain
semesters.

Write
the
relation
as
a
set
of
ordered
pairs
and
find
the
 domain
and
range.
 
 Set
of
ordered
pairs:
 Semester
 #
of
students
 FS07
 1258
 SS08
 247
 FS08
 1061
 Domain:
 
 
 
 
 Range:
 SS09
 245
 
 
 Example
3:

A
particular
relation
is
defined
by
the
following
correspondence
(in
the
 figure).

Write
the
relation
as
a
set
of
ordered
pairs
and
find
the
domain
and
range.
 
 
 
 
 
 
 
 
 
 
 
 
 Set
of
ordered
pairs:
 5
 3
 
 
 
 
 1
 4
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Domain:
 
 
 
 Range:
 2
 7
 
 
 
 
 Page
4
of
5
 MTH
1825
sec.
006
 
 Monday,
Sept.
27,
2010
 Example
4:

Find
the
domain
and
range
(in
interval
notation)
for
each
relation.
 
 a.
 
 
 
 
 
 
 
 
 
 
 
 b.
 
 
 
 
 
 
 
 
 
 
 Domain:
 
 
 
 
 
 
 
 
 



Domain:
 
 
 Range:
 
 
 
 
 
 
 
 
 
 



Range:
 
 
 c.
 
 
 
 
 
 
 
 
 
 
 
 d.
 
 
 
 
 
 
 
 
 
 Domain:
 
 
 
 
 
 
 
 
 



Domain:
 
 
 Range:
 
 
 
 
 
 
 
 
 
 



Range:
 
 
 e.
 
 
 
 
 
 
 
 
 
 
 
 f.
 
 
 
 
 
 
 
 
 
 
 
 
 Domain:
 
 
 
 
 
 
 
 
 Domain:
 
 
 Range:
 
 
 
 
 
 
 
 
 
 Range:
 
 
 Page
5
of
5
 ...
View Full Document

Ask a homework question - tutors are online