Unit 3 Linear Function
Lesson 1 Modeling Linear Relationships
Investigation 2 Symbolize It
Name:__________________________________
Dunking Booth Profit
1. The student council at Eastern High School decided to rent a dunking booth for a fund-raiser.
They were quite sure that students would pay for chances to hit a target with a ball to dunk a
teacher or administrator in a tub of cold water. The dunking booth costs $150 to rent for the
event, and the student council decided to charge students $0.50 per throw.
a. How do you know from the problem description that profit is a linear function of the
number of throws?
b. Use the words NOW and NEXT to write a rule showing how fund-raiser profit changes
with each additional customer.
c. Write a rule that shows how to calculate the profit P in dollars if t throws are
purchased.
d. What do the coefficient of t and the constant term in your rule from Part c tell about:
i. The graph of profit as a function of number of throws?
ii. A table of sample (number of throws, profit) values?
e. What is the profit if:
i. 50 throws are purchased?
ii. 500 throws are purchased?
iii. 5000 throws are purchased?
f. How many throws are needed for a profit of:
i. $0?
ii. $100
iii. $1000
The description of the dunking booth problem included enough information about the relationship
between the number of customers and profit to write the profit function. However, in many
problems, you will have to reason from patterns in a data table or graph to write a function rule.
Arcade Prices
2. Every business has to deal with two important patterns of change, called depreciation and
inflation. When new equipment is purchased, the resale value of
that equipment declines or depreciates as time passes. The cost of
buying new replacement equipment usually increases due to
inflation as time passes. The owners of Game Time, Inc. operate a
chain of video games arcades. They keep a close eye on prices for
new arcade games and the resale values of their existing games.
One set of predictions is shown in the graph below.
a.
Which of the two linear functions predicts the future price
of new arcades games?
Which predicts the future resale value of arcade games that are
purchased now?
b. For each graph:
i. Find the slope and y-intercept. Explain what these values tell about arcade game
prices.
Line I
Slope:
y-intercept:
Line II
Slope:
y-intercept:
ii. Write a rule for calculating game price P in dollars at any future time t in years.
iii. Write a rule for calculating resale price R in dollars at any future time t in years.
c.
What would be the price of the game in 8 years?
d. What would be the resale value of the game in 8 years?
Turtles
3. The Terrapin Candy Company sells its specialty – turtles made from pecans, caramel, and
chocolate – through orders placed online. The company web page shows a table of prices for
sample orders. Each price includes a fixed shipping-and-handling costs plus a cost per box of
candy.
Number of Boxes
1
2
3
4
5
10
Prices (in $)
20
35
50
65
80
155
a. Explain why the price seems to be a linear function of the number of boxes ordered.
b. What is the rate of change in order price as the number of boxes increases?
c. What is the cost of shipping?
d. Write a rule for calculating the price P in dollars for n boxes of turtle candies.
e. Use your rule to find the price for 6 boxes of candies.
f. Use your rule to find the price for 18 boxes of candies.
g. Use your rule to find the price for 42 boxes of candies.
Use your rule to find the number of boxes you can buy for:
h. $125
i. $500
j. $1100