Algebra I: Strand 3. Quadratic and Nonlinear Functions; Topic 3. Exponential; Task 3.3.1
TASK 3.3.1: CALCULATOR MODEL FOR EXPONENTIAL FUNCTIONS
Solutions
1.
Enter the following in your calculator and observe the result.
2
+
Enter
2
3
Enter
5
Enter
Enter
nter
8
Enter
Enter
nter
11
Enter
Enter
nter
14
Enter
Enter
nter
17
Enter
After reaching 17, you lose count so here is a sequence
nter
{1,2}
Enter
Enter
nter
{ANS(1)+1,ANS(2)+3}
{1,2}
The calculator thinks the first number is answer #1
and the second number is answer # 2.
Enter
{2,5}
Enter
Enter
nter
{3,8}
Enter
Enter
nter
{4,11}
Enter
Complete for 7 entries and record in nter
the table.
November 23, 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.
1
Algebra I: Strand 3. Quadratic and Nonlinear Functions; Topic 3. Exponential; Task 3.3.1
Table I
ANS(1)
Process
ANS(2)
1
2
2
2
2+3=2 + 3(1)
5
3
2+3+3=2+3(2)
8
4
2+3+3+3=2+3(3)
11
5
2+3+3+3+3=2+3(4)
14
6
2+3+3+3+3+3=2+3(5)
17
7
2+3+3+3+3+3+3=2+3(6)
20
…
…
…
n
2+3+3+3+…+3=2+3(n-1)
(n-1) factors of 3
2+3(n-1)
Using the graphing calculator, create a scatter plot with an appropriate viewing window.
Sketch your graph:
Identify your window:
Xmin:
-1
Xmax:
10
Xscl:
1
Ymin:
-1
Ymax:
25
Yscl:
1
November 23, 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.
2
Algebra I: Strand 3. Quadratic and Nonlinear Functions; Topic 3. Exponential; Task 3.3.1
2. Enter the following in your calculator and observe the result.
2
Enter
2
*3
Enter
6
Enter
nter
Enter
18
Enter
nter
Enter
54
Enter
nter
Enter
162
Enter
nter
Enter
486
Enter
nter
After reaching 486, you lose count so here is a sequence
{1,2}
Enter
{1,2}
Enter
nter
The calculator thinks the first number is answer #1,
and the second number is answer # 2.
{ANS(1)+1,ANS(2)*3}
Enter
{2,6}
Enter
Enter
nter
{3,18}
Enter
Enter
nter
{4,54}
Enter
Complete for 7 entries and record in nter
the table.
November 23, 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 3. Quadratic and Nonlinear Functions; Topic 3. Exponential; Task 3.3.1
Table II
ANS(1)
Process
ANS(2)
1
2*30
2
2
2*3=2*31
6
3
2*3*3=2*32
18
4
2*3*3*3=2*33
54
5
2*3*3*3*3=2*34
162
6
2*3*3*3*3*3=2*35
486
7
2*3*3*3*3*3*3=2*36
1458
…
…
…
n
2*3*3*3*…*3=2*3(n-1)
(n –1) factors of 3
2*3(n-1)
Using the graphing calculator, create a scatter plot with an appropriate viewing window.
Sketch your graph:
Identify your window:
Xmin:
-1
Xmax:
10
Xscl:
1
Ymin:
-1
Ymax:
500
Yscl:
50
The data is entered as a sequence in order to show the count and the value of the
sequence.
November 23, 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 3. Quadratic and Nonlinear Functions; Topic 3. Exponential; Task 3.3.1
Summary Questions:
1. What operation is repeated in problem 1? repeated addition
2. What kind of function resulted from this operation? linear
3. What operation is repeated in problem 2? repeated multiplication
4. What kind of function resulted from this operation? exponential
& 'y #
5. For table I, use the graphing calculator to enter the change $ ! in L3.
% 'x "
The ΔList key is found under 2nd STAT OPS #7
6. Using the graphing calculator, find the ratio of consecutive terms from Table II. In
order to find consecutive ratios in a list:
1. First copy and paste the list into a blank list.
2. Delete the first term on L2 and delete the last term on L3
3. Arrow over to L4 and divide L2 by L3 to
find the common ratio.
November 23, 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.
5
Algebra I: Strand 3. Quadratic and Nonlinear Functions; Topic 3. Exponential; Task 3.3.1
TASK 3.3.1: CALCULATOR MODEL FOR EXPONENTIAL FUNCTIONS
1.
Enter the following in your calculator and observe the result.
2
+
Enter
2
3
Enter
5
Enter
Enter
nter
8
Enter
Enter
nter
11
Enter
Enter
nter
14
Enter
Enter
nter
17
Enter
After reaching 17, you lose count so here is a sequence
nter
{1,2}
Enter
Enter
nter
{ANS(1)+1,ANS(2)+3}
{1,2}
The calculator thinks the first number is answer #1
and the second number is answer # 2.
Enter
{2,5}
Enter
Enter
nter
{3,8}
Enter
Enter
nter
{4,11}
Enter
Complete for 7 entries and record in nter
the table.
November 23, 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.
6
Algebra I: Strand 3. Quadratic and Nonlinear Functions; Topic 3. Exponential; Task 3.3.1
Table I
ANS(1)
Process
ANS(2)
1
2
3
4
5
6
7
…
…
n
Using the graphing calculator, create a scatter plot with an appropriate viewing window.
Sketch your graph:
Identify your window:
Xmin:
Xmax:
Xscl:
Ymin:
Ymax:
Yscl:
November 23, 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.
7
Algebra I: Strand 3. Quadratic and Nonlinear Functions; Topic 3. Exponential; Task 3.3.1
2. Enter the following in your calculator and observe the result.
2
Enter
2
*3
Enter
6
Enter
nter
Enter
18
Enter
nter
Enter
54
Enter
nter
Enter
162
Enter
nter
Enter
486
Enter
After reaching 486, you lose count so here is a sequence
nter
{1,2}
Enter
{1,2}
Enter
nter
The calculator thinks the first number is answer #1,
and the second number is answer # 2.
{ANS(1)+1,ANS(2)*3}
Enter
{2,6}
Enter
Enter
nter
{3,18}
Enter
Enter
nter
{4,54}
Enter
Complete for 7 entries and record in the table.
nter
November 23, 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.
8
Algebra I: Strand 3. Quadratic and Nonlinear Functions; Topic 3. Exponential; Task 3.3.1
Table II
ANS(1)
Process
ANS(2)
1
2
3
4
5
6
7
…
…
n
Using the graphing calculator, create a scatter plot with an appropriate viewing window.
Sketch your graph:
Identify your window:
Xmin:
Xmax:
Xscl:
Ymin:
Ymax:
Yscl:
The data is entered as a sequence in order to show the count and the value of the
sequence.
November 23, 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.
9
Algebra I: Strand 3. Quadratic and Nonlinear Functions; Topic 3. Exponential; Task 3.3.1
10
Summary Questions:
1. What operation is repeated in problem 1?
2. What kind of function resulted from this operation?
3. What operation is repeated in problem 2?
4. What kind of function resulted from this operation?
& 'y #
5. For table I, use the graphing calculator to enter the change $ ! in L3.
% 'x "
6. Using the graphing calculator, find the ratio of consecutive terms from Table II.
November 23, 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.