Transcript Linear Models

Linear Models
Create a scatterplot of the population for North Carolina on
your graphing calculator.
Year
Population
(millions)
2003
8.41
2004
8.52
2005
8.66
2006
8.85
2007
9.04
2008
9.22
Linear Models
Define the variables
t = years since 2000
P = population of North Carolina in millions
Linear Models: TI –84
Input data:
 Go to STAT and 1:Edit
 Go to the top of L1 and clear
 Go to the top of L2 and clear
L1 represents x or horizontal axis
L2 represents y or vertical axis
 Go to L1 and enter the values
 Go to L2 and enter the values on the
table
Linear Models: TI –84
Domain/Range
Select WINDOW and you will see:
Xmin = smaller than smallest input
Xmax= larger than largest input
Xscal=
Ymin= smaller than the smallest output
Ymax= larger than largest output
Yscal=
Each will be based on the domain and range of the
values from the table.
Linear Models: TI –84
Graphing Points
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Enter 2nd and y =
A screen with STAT PLOTS
Choose 1: Plot 1 enter
Make sure Plot 1 is on and the X list is designated L1
Y list: L2
Also make sure Type: shows scatter plot.
Finally select Graph and the plot will show on the
screen.
Graphing Line on TI- 84
•
Choose the two points that will make the line the
best fit, and solve for the equation
• 8.41 – 9.04
3 - 7
m = 0.1575 (round to nearest hundredth)
Y-intercept y = 0.16x + b
8.41 = 0.16(3) + b
8.41 = 0.48 + b
7.93 = b
Graphing Line on TI- 84
y = 0.16x + 7.93
Select y = , button
Enter the equation found 0.16x + 7.93
Use the X,T,ϴ,n button to insert x into the
equation.
Once the equation is entered select GRAPH
A line will be drawn through the points that
were previously plotted.
Total Revenue for GE
Year
2004
2005
2006
2007
2008
Revenue
(Billions $)
124
136
152
172
183
a) Find an equation for a
model of these data.
b) Using your model,
estimate GE’s revenue
in 2010
c)What is the slope of
your model?
What does it mean in
regard to GE’s revenue
Relation
Relationship between elements of a set of
input and elements of a set of outputs
(2,3)
x + 2y = 12
Relates x-values
with y-values
using arithmetic
operation
Function
For every input there is only one output
{(1,2) , (3,4) , (5, 6) , (7,8)}
Input
1
2
3
Output
5
6
7
x
y
1
5
2
5
3
5
Function or Not?
• The set A = {(2,5) , (4,8) , (10,8) , (20, 15)}
• Weekly salaries during the mth month of the
year.
Day of week
Monday
Wednesday
Saturday
Monday
Temperature
F
90
88
91
93
Notation
f(x)
“f of x”
Represents a function named f that
depends on the variable x
f means output/y-variable/range
Shorthand method of providing information
in a compact form.
Word problems and Function
Notation
a)
H(t) = height of a toy rocket in feet t seconds after
launch.
What does H(3) = 12 mean?
b) C(m) = Cost in hundred of dollars for producing m miracle
mops.
C (2500) = 189
c) P(t) = population of Michigan, in millions, t, years since
2000.
P(10) = 10.4
Population of Wisconsin, in millions
• Find an equation for a
model of these data. Write
your model in function
notation.
• Determine a reasonable
domain and range
• Find P(14) and interpret
its meaning in regard to
the pop of Wisconsin.
Year
2003
2004
2005
2006
2007
2008
Population
(millions)
5.47
5.51
5.54
5.57
5.60
5.63
Review
• f(x) = 4x + 3
f(3)
Domain and range is not restricted
Word problems Domain and range is set by
the problem.
Systems of Equations
Set of equations that require a solution that will
work for all of the equations in the set.
y= x + 4
y = 2x – 8
• Table
x
y=x+4
x
2
2
4
4
6
6
y = 2x - 8
• Graph find the slope and y-intercept for
each line
Practice
• Your company wants to print some flyers
for advertising a new product. The printer
has two options to produce the flyers, The
traditional printing cost is $250 for setup
and $0.15 per page printed. To print the
flyers digitally, they charge $50 for setup
and $0.20 per printed page.
Types of Systems
Consistent
Inconsistent
Algebraic Methods of solving
systems
• Substitution
y = 4x –5
y = x + 22
Replace the expression of a variable in one
equation into another.
Substitution
• Geothermal and wind energy, find the year
when the amount of geothermal and wind
energy produced will be the same.
G(t) = -0.08t + 5.68
W(t) = 0.82t – 1.03