Notes: Recreation Application

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Objectives
Translate between the various representations of
functions. Solve problems by using the various
representations of functions.
Notes Recreation Application
Janet is rowing across an 80-meter-wide river at
a rate of 3 meters per second. A) Create a
table B) Write an equation (linear, quadratic or
exponential), C) Graph of the distance that
Janet has remaining before she reaches the other
side. D) When will Janet reach the shore?
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An amusement park manager estimates daily profits
by multiplying the number of tickets sold by 20.
This verbal description is useful, but other
representations of the function may be more
useful.
These different representations can help the
manager set, compare, and predict prices.
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Example 1 Business Application
Sketch a possible graph to represent the
following.
Ticket sales were good until a massive power
outage happened on Saturday that was not repaired
until late Sunday.
The graph will show decreased sales until Sunday.
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Example 2A
What if ? Sketch a possible graph to represent
the following.
The weather was beautiful on Friday and Saturday,
but it rained all day on Sunday and Monday.
The graph will show decreased sales on Sunday and
Monday.
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Example 2B
Sketch a possible graph to represent the
following.
The graph will show decreased sales on Friday and
Sunday.
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Because each representation of a function (words,
equation, table, or graph) describes the same
relationship, you can often use any
representation to generate the others.
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Example 3 Using Multiple Representations to
Solve Problems
A hotel manager knows that the number of rooms
that guests will rent depends on the price. The
hotels revenue depends on both the price and the
number of rooms rented. The table shows the
hotels average nightly revenue based on room
price. Use a graph and an equation to find the
price that the manager should charge in order to
maximize his revenue.
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Example 3A Continued
Does the data does appear linear, quadratic or
exponential?
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Example 3B Using Multiple Representations to
Solve Problems
An investor buys a property for 100,000. Experts
expect the property to increase in value by about
6 per year. Use a table, a graph and an equation
to predict the number of years it will take for
the property to be worth more than 150,000.
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Example 3B Continued
Make a table for the property. Because you are
interested in the value of the property, make a
graph, by using years t as the independent
variable and value as the dependent variable.
Identify as linear, quadratic, or exponential.
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Review Example 4A
4A. The graph shows the number of cars in a high
school parking lot on a Saturday, beginning at 10
A.M. and ending at 8 P.M. Give a possible
interpretation for this graph.
Possible answer Football practice goes from
1100 A.M. until 100 P.M. Families begin
arriving at 400 P.M. for a play that begins at
500 P.M. and ends at 700 P.M. After the play,
most people leave.
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Review
4B. An online computer game company has 10,000
subscribers paying 8 per month. Their research
shows that for every 25-cent reduction in their
fee, they will attract another 500 users. Use a
table and an equation (linear, quadratic or
exponential) to find the fee that the company
should charge to maximize their revenue.
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Notes Recreation Application
Janet is rowing across an 80-meter-wide river at
a rate of 3 meters per second. A) Create a
table B) Write an equation (linear, quadratic or
exponential), C) Graph of the distance that
Janet has remaining before she reaches the other
side. D) When will Janet reach the shore?
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Notes
A. Create a table.
Let t be the time in seconds and d be Janets
distance, in meters, from reaching the
shore. Janet begins at a distance of 80 meters,
and the distance decreases by 3 meters each
second.
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Notes
B. Write an equation.
d 80
3t
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Notes
D Find the intercepts and graph the equation.
d-intercept80
Solve for t when d 0
d 80 3t
0 80 3t