November 20, 2015
3.1 Linear Functions
and Their Properties
Day 2
Objectives: Build linear models from verbal descriptions.
November 20, 2015
Example 1: The cost C, in dollars, of renting a moving
truck for a day is modeled by the function C(x) = 0.07x +
29, where x is the number of miles driven.
a) What is the cost if you drive 110 miles?
b) If the cost of renting the moving truck is $100, how many miles did
you drive?
c) Suppose that you want the cost to be no more that $40. What is
the maximum number of miles that you can drive?
d) What is the implied domain of C?
e) Interpret the slope
f) Interpret the y-intercept
49 (37)
November 20, 2015
Example 1: Suppose that the quantity supplied S and quantity
like 39
demanded D of hotdogs at a baseball game are given by the
following functions:
S(p) = -2000 + 3000p
D(p) = 10000 - 1000p
where p is the price in dollars. The equilibrium price of a market
is defined as the price at which quantity supplied equals quantity
demanded (S = D).
a. Find the equilibrium price for hot dogs at the baseball game. What is
the equilibrium quantity?
b. Determine the price for which quantity demanded is less than
quantity supplied.
c. What do you think would eventually happen to the price of hot dogs
is quantity demanded is less than quantity supplied?
November 20, 2015
Example 2: Suppose that a company just purchased a fleet of new
cars for it's sales force at a cost of $28,000 per car. The company chooses
to depreciate each vehicle using the straight-line method over 7 years.
This means the car will depreciate by $28,000/7 = $4000 per year.
a. Write a linear fcn that expresses the book value V of each car as a
function of its age, x.
b. What is the implied domain of the function found in part (a).
c. Graph the function.
d. What is the book value of each car after 3 years?
e. Interpret the slope.
f. When will the book value of each car be $8000?
EX 4
November 20, 2015
like 47
Example 3: The simplest cost function is the linear cost function,
C(x)=mx+b, where the y-intercept b represents the fixed costs of operating
a business and the slope m represents the cost of each item produced.
Suppose that a video game manufacturer has daily fixed costs of $520
and each video game costs $8 to manufacture.
a. Write a linear model that expresses the cost C of manufacturing x video
games in a day.
b. Graph the model.
c. What is the cost of manufacturing 100 video games in a day?
d.How many video games can be manufactured for $3225?
November 20, 2015
Example 5: The following data represent the various combinations of
soda and hot dogs that Holly can buy at a baseball game with $60.
a. Plot the ordered pairs (s,h) in a Cartesian plane.
b. Show that the number of hot dogs purchased h is a linear function of the
number of sodas purchased s.
c. Determine the linear function that describes the relation between s and h.
(Use a point and slope found, from (b))
d.What is the implied domain of the linear function?
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November 20, 2015
e. Graph the linear function in the Cartesian drawn in part (a).
f. Interpret the slope.
g. Interpret the values of the intercepts.
November 20, 2015
Homework
pg. 137-139: # 37, 39, 45, 47, 51
November 20, 2015
Answers to example 3:
(a)
(d)
(e)
(f)