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Andre and Kara are collecting food for the food pantry in their neighborhood. For every person they ask to donate, they receive an average of 13 items. Create a table and graph an arithmetic sequence to model this scenario. What would be the most appropriate label for the y-axis?(1 point)

Responses

neighborhood population
neighborhood population

number of people asked to donate
number of people asked to donate

number of items donated
number of items donated

food pantry

Eric has $27.00 and wants to buy comic books. If each comic book costs $4.00, create a table and graph the arithmetic sequence to display how much money Eric has left after each comic book purchase.

To show that arithmetic sequence formulas have the same structure as linear functions, choose the linear function equation that has the same structure as the arithmetic sequence an=6+(n−1)⋅8
.(1 point)
Responses

y=6x+8
y equals 6 x plus 8

y=2x−8
y equals 2 x minus 8

y=8x+6
y equals 8 x plus 6

y=8x−2

Use the table to answer the question.

x y
2 a
4 b
Use the arithmetic sequence formula an=−8+(n−1)⋅2
to find the missing values in the table.

(1 point)
Responses

a=−12; b=−10
a equals negative 12 ; b equals negative 10

a=−6; b=−2
a equals negative 6 ; b equals negative 2

a=−10; b=−8
a equals negative 10 ; b equals negative 8

a=−15; b=−13

Alex and Jesse are baking holiday muffins. On day one, they baked five muffins, on day two, they baked 11 muffins, and on day three, they baked 17 muffins. What is the slope for this arithmetic sequence?(1 point)
Responses

−1
negative 1

6
6

1
1

−6

1 answer

Let's address each question one by one.

1. Andre and Kara's Food Donation

Most appropriate label for the y-axis:

  • Since the scenario involves the number of items donated based on the number of people asked to donate, the most appropriate label for the y-axis would be:

Response: number of items donated

Table and Graph for Number of Items Donated

To create a table, we can establish the relationship as follows:

  • If \(n\) is the number of people asked to donate, the number of items donated would be \(13n\).

Example Table: | Number of People Asked (n) | Number of Items Donated (13n) | |-----------------------------|-------------------------------| | 1 | 13 | | 2 | 26 | | 3 | 39 | | 4 | 52 | | 5 | 65 |

2. Eric's Comic Book Purchases

Eric has $27.00 and each comic book costs $4.00.

Table for Money Left: After each comic book purchase, the remaining money can be computed as follows:

  • After 0 books: $27.00
  • After 1 book: $27.00 - $4.00 = $23.00
  • After 2 books: $23.00 - $4.00 = $19.00
  • After 3 books: $19.00 - $4.00 = $15.00
  • After 4 books: $15.00 - $4.00 = $11.00
  • After 5 books: $11.00 - $4.00 = $7.00
  • After 6 books: $7.00 - $4.00 = $3.00
  • After 7 books: $3.00 - $4.00 = -$1.00 (not enough funds)

Here is the corresponding table:

| Number of Comics Purchased | Money Left ($) | |---------------------------|-----------------| | 0 | 27 | | 1 | 23 | | 2 | 19 | | 3 | 15 | | 4 | 11 | | 5 | 7 | | 6 | 3 | | 7 | -1 |

3. Arithmetic Sequence Formula

Given the formula \(a_n = 6 + (n - 1) \cdot 8\), we can rewrite it as \(a_n = 8n - 2\). The structure of this arithmetic sequence can be compared to a linear equation.

Choose the linear function equation:

  • The best fit would be:

Response: y = 8x - 2

4. Use the Arithmetic Sequence Formula

Given the sequence formula \(a_n = -8 + (n - 1) \cdot 2\):

  • For n = 2: \[ a_2 = -8 + (2 - 1) \cdot 2 = -8 + 2 = -6 \quad \Rightarrow a = -6 \]

  • For n = 4: \[ a_4 = -8 + (4 - 1) \cdot 2 = -8 + 6 = -2 \quad \Rightarrow b = -2 \]

Response: a = -6; b = -2

5. Slope for Alex and Jesse's Muffin Baking

To find the slope of the arithmetic sequence between the days:

| Day | Muffins Baked | |-----|---------------| | 1 | 5 | | 2 | 11 | | 3 | 17 |

The change in muffins (output) over change in days (input): \[ \text{slope} = \frac{(17 - 5)}{(3 - 1)} = \frac{12}{2} = 6 \]

Response: 6

Summary of all Responses:

  1. Number of items donated
  2. No need for response here as it's just data
  3. y = 8x - 2
  4. a = -6; b = -2
  5. 6