Transcript Section 2.4 Linear Functions and Models

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P. 102 15 – 60 5ths
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APPLY LINEAR FUNCTIONS
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X-axis time since purchase
Y-axis value
Use two intercepts (0, initial value) and (time
until value is zero, 0) to form line
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A company buys a new company car for $28,000. The
company will replace this new car in seven years.
a.
Find the equation of the straight line depreciation.
b.
Graph the line.
c.
What is the “book-value” of the car after three years?
d.
Interpret the slope of the line.
e.
When will the book value of the car be $8000?
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Equilibrium price – price at which supply is equal to
demand.
Supply - The quantity supplied of a good is the
amount of a product that a company is willing to
make available for sale at a given price. The supply
function is named S(p).
Demand - The quantity demanded of a good is the
amount of a product that consumers are willing to
purchase at a given price. The demand function is
named D(p).
Suppose that the quantity supplied, S, and quantity
demanded, D, of cellular telephones each month
are given by the following functions:
S(p) = 60P – 900
D(p) = -15p + 2850
Where p is the price (in dollars) of the telephone.
a.
What is the equilibrium price?
b.
Determine the prices at which supply is greater
than demand. That is solve S(p) > D(p).
c.
Graph the supply and demand functions and label
the equilibrium price.
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LINEAR REGRESSION
(a) Draw a scatter
diagram of the data,
treating on-base
percentage as the
independent variable.
(b) Use a graphing utility
to draw a scatter
diagram.
(c) Describe what happens
to runs scored as the
on-base percentage
increases.
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LINEAR – positive, negative, constant
NONLINEAR
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Eye-ball method
Enter data into list
Make scatterplot
Select to “representative” points
Find line using these two points
(a)Select two points and find
an equation of the line
containing the points.
(b) Graph the line on the
scatter diagram obtained in
the previous example.
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Use the eye-ball method to find the line of
best fit.
Enter data into list
Go to STAT
Go to CALC
Go to LINREG
(a) Use a graphing utility to find
the line of best fit that models
the relation between on-base
percentage and runs scored.
(b) Graph the line of best fit on the
scatter diagram obtained in the
previous example.
(c) Interpret the slope.
(d) Use the line of best fit to
predict the number of runs a
team will score if their on-base
percentage is 33.5.
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Use your calculator
to find the line of
best fit.
Age
(months)
36
Height
(cm)
86
48
90
51
91
54
93
57
94
60
95