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Learning Math Home
Patterns, Functions, and Algebra
 
Session 7 Part A Part B Part C Part D Homework
 
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A B C D
Homework

Video

Solutions for Session 7, Part C

See solutions for Problems: C1 | C2 | C3 | C4 | C5 | C6| C7 | C8 | C9


Problem C1

<< back to Problem C1


 

Problem C2

Here is the completed table:

 

Number of dots on side of square

 

Total number of dots (square number)

1

 

1

2

 

4

3

 

9

4

 

16

5

 

25

6

 

36

10

 

100

13

 

169

 

<< back to Problem C2


 

Problem C3

It is neither a linear nor an exponential graph. Its successive outputs do not have the same ratio; therefore, it cannot be an exponential graph. It is certainly not a straight line, because successive outputs do not have the same difference, so it cannot be a linear graph.

<< back to Problem C3


 

Problem C4

The rule is O = n2, where O is the output, the total number of dots, and n is the number of dots on the side of a square. A recursive rule is Dn = Dlast + (2n - 1).

<< back to Problem C4


 

Problem C5

<< back to Problem C5


 

Problem C6

Here is the completed table.

 

Number of dots on side of triangle

 

Total number of dots (triangular number)

1

 

1

2

 

3

3

 

6

4

 

10

5

 

15

6

 

21

9

 

45

19

 

190

 

<< back to Problem C6


 

Problem C7

As with Problem C3, the graph does not demonstrate exponential behavior, because successive terms do not have the same ratio. It's not a linear graph, either, because it is certainly not a straight line. Actually, the graphs of the table of square numbers and the table of triangular numbers look pretty similar.

<< back to Problem C7


 

Problem C8

There is more than one answer, but one is O = (n)(n + 1) / 2. The recursive form is easier to find: Dn = Dlast + n, because n new dots are added in the nth triangle.

<< back to Problem C8


 

Problem C9

Both closed-form rules involve multiplying n by itself at some point, and both recursive rules involve adding something linear to n. Compare this to linear functions, which have only a single use of the variable in their closed-form rules, and a constant in the recursive rule.

<< back to Problem C9

 

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