# Complete the tables to show how much money would be received for both payment

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Graded Assignment

Extended Problems: Sequences

Solve the problems. When you have finished, submit this assignment to your teacher by the due date for full credit.

An employer provides two payment options for employees.

Option A: Receive $200 the first week. Receive an additional $50 for each of the following weeks.

Option B: Receive $200 the first week. Receive an additional 10% for each of the following weeks.

(2 points)

Score

1. Complete the tables to show how much money would be received for both payment options, each week, for 6 weeks.

Option A

Week

1

2

3

4

5

6

Amount paid

Option B

Week

1

2

3

4

5

6

Amount paid

Answer:

(8 points)

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2. Suppose you are a new employee. You notice that each payment option describes a sequence and decide to use rules to help determine which option to take.

(a) Determine the iterative rule for each sequence. Show your work.

(b) Your friend trusts your tables in Problem 1, but wonders if you wrote the iterative rules correctly. Show two calculations to convince your friend that both your rules work.

Answer:

(5 points)

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3. Consider the iterative rules you wrote in Problem 2.

(a) Explain why the rules are functions.

(b) Your friend says that because the rules are functions, they can be graphed and must have y-intercepts. How would you respond to your friend’s comment?

(c) Your friend uses your rules to determine the outputs when the inputs are 18.5. Explain why her outputs are meaningless in this situation. What would you tell her about the inputs she can use?

Answer:

4. The longest amount of time employees can work under Option A or Option B is 20 weeks. After employees work 20 weeks, they can either quit or keep making the same amount they made during Week 20. If an employee plans on quitting after 20 weeks, which payment option gives the greatest total income? Explain.

Answer:

Your Score

___ of 20

Two supermarket employees, Casey and Jesse, each create a display of stacked soup cans. In Casey’s display, each row has 2 fewer cans than the row below it, and the bottom row has 24 cans. In Jesse’s display, each row has 24 cans.

(4 points)

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5. In both displays, the number of cans in each row forms a sequence. Let the bottom row of each display be Row 1.

(a) Write the recursive rule for each sequence.

(b) Write the iterative rule for each sequence. Show your work.

Answer:

(6 points)

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6. Casey continued her pattern, from the ground up, for as long as she could.

(c) All the cans in Casey’s display have a height of 6 in. How tall is Casey’s display? Show your work or explain your reasoning.

(d) Both Casey’s and Jesse’s displays have the same number of rows. Determine the practical domain and range of each iterative sequence.

Answer:

(5 points)

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7. The differences between the number of cans in each row of Jesse’s display and the number of cans in each row of Casey’s display form a sequence. Let the difference in the bottom row be the first term.

(d) Write the first 5 terms of the sequence. Show or explain how you determined the terms.

(e) Write the iterative rule for the sequence. Show your work. Then demonstrate that your rule works by using it to find the difference in the number of cans in the bottom rows of the two displays and the difference in the number of cans in the top rows of the two displays.

Answer:

(5 points)

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4. Reflection: Look back at Problem 1. Suppose you let the top row in each display be Row 1. How would the recursive and iterative rules be different? Name a benefit of letting the top row be Row 1. Name a benefit of letting the bottom row be Row 1.

Answer:

Your Score

___ of 20

A book club began its first year with 40 members. Once a year, the book club accepts new members. The club’s president anticipates that the number of members will grow as shown in the table.

Year

1

2

3

4

5

6

7

8

Number of members

40

44

48

53

59

64

70

77

(5 points)

Score

8. The club’s president completed the table by using a geometric sequence rule and rounding as needed.

(c) What number did the president use for the common ratio? What is the anticipated growth rate?

(d) Write the iterative rule for the sequence. Then use the rule to determine the anticipated number of members in the club in Year 10. Show your work.

Answer:

(4 points)

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9. The sequence representing the anticipated number of book club members each year is a function.

(e) Nathan says, “When the input is 3.5, the output is about 51.” What would you tell Nathan about his statement?

(f) Peggy says, “The y-intercept of the sequence is about 36.” What would you tell Peggy about her statement?

Answer:

(6 points)

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10. After the club president made the table in Problem 1, she realized that she did not account for members leaving the club. She anticipates that after the first year, the book club will lose 3 members per year.

(f) The total number of members the president anticipates losing, from the first year through a given year, forms a sequence. Write the iterative rule for the sequence. Show your work.

(g) The book club will have a party when the number of members reaches 100. Use iterative rules to predict when this party will be held. Show your work.

Answer:

(5 points)

Score

5. Reflection: Look back at Problem 1. Suppose the club’s president completed the table by using an exponential growth function. How would the exponential growth function compare to the iterative sequence rule? How would the meaning of the inputs differ?

Answer:

Your Score

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