1
Algebra I: Strand 1. Foundations of Functions; Topic 2. Independent and Dependent; Task 1.2.6
TASK 1.2.6: CAGE THE CATS
Solutions
Cage the Cats
The Humane Society of Catsville has to make a yearly budget for new equipment. A
necessary item for the organization is cages to isolate new felines. The cats are isolated
in order to prevent the spread of diseases and parasites. They only have 23 usable cages
at the present time. The manager predicts that the humane society will need 5 new cages
each month. Describe the function that models this situation. Complete a data table for
the information; write an algebraic expression, and draw a scatter plot for the situation.
Be sure to label the axes of the graph. How many months will it take the humane society
to collect 323 cages?
The number of cages depends on the usable cages at the current time plus adding five
new cages each month.
OR
The number of cages depends on the number of months.
OR
Starting with 23 cages, the humane society will add 5 new cages each month.
Months
1
2
3
4
Process
23 + 5 (1)
23 + 5 (2)
x
23 + 5x
Total Number of Cages
28
33
38
43
y=23+5x
November 12, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University
of Texas at Austin for the Texas Higher Education Coordinating Board.
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Algebra I: Strand 1. Foundations of Functions; Topic 2. Independent and Dependent; Task 1.2.6
Cage the Cats
Total Number of Cages
60
50
40
30
20
10
0
0
1
2
3
4
5
6
Number of Months
323=23 + 5x
x=60
It will take 60 months or 5 years to collect 323 cages.
November 12, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University
of Texas at Austin for the Texas Higher Education Coordinating Board.
3
Algebra I: Strand 1. Foundations of Functions; Topic 2. Independent and Dependent; Task 1.2.6
Teaching notes
There are a variety of ways to describe the function relationship between the number of
cages and the number of months. Data tables may vary; however, each should show the
number of months as the independent variable and the number of cages as the dependent
variable. Check to make sure the scatter plot has axes labeled correctly.
November 12, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University
of Texas at Austin for the Texas Higher Education Coordinating Board.
4
Algebra I: Strand 1. Foundations of Functions; Topic 2. Independent and Dependent; Task 1.2.6
TASK 1.2.6: CAGE THE CATS
Cage the Cats
The Humane Society of Catsville has to make a yearly budget for new equipment. A
necessary item for the organization is cages to isolate new felines. The cats are isolated
in order to prevent the spread of diseases and parasites. They only have 23 usable cages
at the present time. The manager predicts that the humane society will need 5 new cages
each month. Describe the function that models the situation. Complete a data table for
the information; write an algebraic expression, and draw a scatter plot for the situation.
Be sure to label the axis of the graph. How many months will it take the humane society
to collect 323 cages?
November 12, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University
of Texas at Austin for the Texas Higher Education Coordinating Board.