Math / Algebra

QuestionPractice (cont'd) They decide to ack of 18 of their favourite mini chocolate bars eat 2 bars each day. a) Represent the of chocolat the pattern in the number the table and bars left by completing \begin{tabular}{|c|c|} \hline \begin{tabular}{c} Days after \\ purchase, $x$ \end{tabular} & \begin{tabular}{c} Chocolate \\ bars left, $y$ \end{tabular} \\ \hline 0 & 18 \\ \hline 1 & \\ \hline 2 & \\ \hline 3 & \\ \hline \end{tabular} b) How many chocolate bars would be left after 5 days? Explain how you know. c) Suppose Ryley eats 3 bars each day rather than 2. What would be the first 4 terms of the new pattern? How would the graph change? logy 8, Pattems and Relations The right to reproduce or modify this page is restricted to purchasing school onvrioht Q 2023 Pearsm Canarla ine: This naoe mav have heen modified from its nrinin

Studdy Solution

STEP 1

What is this asking? Ryley and a friend buy 18 chocolate bars and eat 2 each day.
We need to figure out how many bars are left after some days, what happens if they eat 3 bars a day instead, and how that changes things. Watch out! Make sure to count the chocolate bars correctly and don't mix up the different eating rates.

STEP 2

1. Complete the Table
2. Calculate Bars Left After 5 Days
3. Find the New Pattern with 3 Bars Eaten Daily
4. Describe the Graph Change

STEP 3

Initially, they have $\$18$ chocolate bars.
This is our initial value when $x = 0$ days have passed.

STEP 4

They eat $2$ bars a day, so after $1$ day, they have $18 - 2 = 16$ bars left.

STEP 5

After $2$ days, they've eaten $2 \cdot 2 = 4$ bars total, leaving $18 - 4 = 14$ bars.

STEP 6

After $3$ days, they've eaten $3 \cdot 2 = 6$ bars, leaving $18 - 6 = 12$ bars.

STEP 7

So our table looks like this:
$\begin{array}{cc} \text{Days after purchase, } x & \text{Chocolate bars left, } y \\ 0 & 18 \\ 1 & 16 \\ 2 & 14 \\ 3 & 12 \\ \end{array}$

STEP 8

They eat 2 bars each day.
After 4 days, $18 - (4 \cdot 2) = 10$ bars.
After 5 days, $18 - (5 \cdot 2) = 8$ bars.

STEP 9

They start with $\$18$ bars.

STEP 10

Eating $3$ bars a day, after $1$ day, $18 - 3 = 15$ bars remain.

STEP 11

After $2$ days, $18 - (2 \cdot 3) = 12$ bars remain.

STEP 12

After $3$ days, $18 - (3 \cdot 3) = 9$ bars remain.

STEP 13

The new pattern is 18, 15, 12, 9...

STEP 14

The original graph decreases by $2$ bars per day.
The new graph decreases by $3$ bars per day.

STEP 15

The new graph would be steeper because the number of chocolate bars decreases more quickly.

STEP 16

a) The completed table is shown above in step 2.1.5. b) After 5 days, there will be $8$ chocolate bars left.
We found this by subtracting $2$ bars for each day from the initial $18$ bars. c) The first four terms of the new pattern are 18, 15, 12, and 9.
The graph would be steeper, showing a faster decrease in the number of chocolate bars.

Was this helpful?

Studdy Solution

STEP 1

STEP 2

1. Complete the Table
2. Calculate Bars Left After 5 Days
3. Find the New Pattern with 3 Bars Eaten Daily
4. Describe the Graph Change

STEP 3

Initially, they have $\$18$ chocolate bars.
This is our initial value when $x = 0$ days have passed.

STEP 4

They eat $2$ bars a day, so after $1$ day, they have $18 - 2 = 16$ bars left.

STEP 5

After $2$ days, they've eaten $2 \cdot 2 = 4$ bars total, leaving $18 - 4 = 14$ bars.

STEP 6

After $3$ days, they've eaten $3 \cdot 2 = 6$ bars, leaving $18 - 6 = 12$ bars.

STEP 7

So our table looks like this:
$\begin{array}{cc} \text{Days after purchase, } x & \text{Chocolate bars left, } y \\ 0 & 18 \\ 1 & 16 \\ 2 & 14 \\ 3 & 12 \\ \end{array}$

STEP 8

They eat 2 bars each day.
After 4 days, $18 - (4 \cdot 2) = 10$ bars.
After 5 days, $18 - (5 \cdot 2) = 8$ bars.

STEP 9

They start with $\$18$ bars.

STEP 10

Eating $3$ bars a day, after $1$ day, $18 - 3 = 15$ bars remain.

STEP 11

After $2$ days, $18 - (2 \cdot 3) = 12$ bars remain.

STEP 12

After $3$ days, $18 - (3 \cdot 3) = 9$ bars remain.

STEP 13

The new pattern is 18, 15, 12, 9...

STEP 14

The original graph decreases by $2$ bars per day.
The new graph decreases by $3$ bars per day.

STEP 15

The new graph would be steeper because the number of chocolate bars decreases more quickly.

STEP 16

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

STEP 2

1. Complete the Table2. Calculate Bars Left After 5 Days3. Find the New Pattern with 3 Bars Eaten Daily4. Describe the Graph Change

STEP 3

Initially, they have $18\$18$18 chocolate bars.This is our **initial value** when x=0x = 0x=0 days have passed.

STEP 4

They eat 222 bars a day, so after 111 day, they have 18−2=1618 - 2 = 1618−2=16 bars left.

STEP 5

After 222 days, they've eaten 2⋅2=42 \cdot 2 = 42⋅2=4 bars total, leaving 18−4=1418 - 4 = 1418−4=14 bars.

STEP 6

After 333 days, they've eaten 3⋅2=63 \cdot 2 = 63⋅2=6 bars, leaving 18−6=1218 - 6 = 1218−6=12 bars.

STEP 7

So our table looks like this:Days after purchase, xChocolate bars left, y018116214312\begin{array}{cc} \text{Days after purchase, } x & \text{Chocolate bars left, } y \\ 0 & 18 \\ 1 & 16 \\ 2 & 14 \\ 3 & 12 \\ \end{array}Days after purchase, x0123​Chocolate bars left, y18161412​

STEP 8

They eat 2 bars each day.After 4 days, 18−(4⋅2)=1018 - (4 \cdot 2) = 1018−(4⋅2)=10 bars.After 5 days, 18−(5⋅2)=818 - (5 \cdot 2) = 818−(5⋅2)=8 bars.

STEP 9

They start with $18\$18$18 bars.

STEP 10

Eating 333 bars a day, after 111 day, 18−3=1518 - 3 = 1518−3=15 bars remain.

STEP 11

After 222 days, 18−(2⋅3)=1218 - (2 \cdot 3) = 1218−(2⋅3)=12 bars remain.

STEP 12

After 333 days, 18−(3⋅3)=918 - (3 \cdot 3) = 918−(3⋅3)=9 bars remain.

STEP 13

The new pattern is 18, 15, 12, 9...

STEP 14

The original graph decreases by 222 bars per day.The new graph decreases by 333 bars per day.

STEP 15

The new graph would be *steeper* because the number of chocolate bars decreases more quickly.

STEP 16

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Complete the Table
2. Calculate Bars Left After 5 Days
3. Find the New Pattern with 3 Bars Eaten Daily
4. Describe the Graph Change

Initially, they have $\$18$ chocolate bars.
This is our initial value when $x = 0$ days have passed.

They eat $2$ bars a day, so after $1$ day, they have $18 - 2 = 16$ bars left.

After $2$ days, they've eaten $2 \cdot 2 = 4$ bars total, leaving $18 - 4 = 14$ bars.

After $3$ days, they've eaten $3 \cdot 2 = 6$ bars, leaving $18 - 6 = 12$ bars.

So our table looks like this:
$\begin{array}{cc} \text{Days after purchase, } x & \text{Chocolate bars left, } y \\ 0 & 18 \\ 1 & 16 \\ 2 & 14 \\ 3 & 12 \\ \end{array}$

They eat 2 bars each day.
After 4 days, $18 - (4 \cdot 2) = 10$ bars.
After 5 days, $18 - (5 \cdot 2) = 8$ bars.

They start with $\$18$ bars.

Eating $3$ bars a day, after $1$ day, $18 - 3 = 15$ bars remain.

After $2$ days, $18 - (2 \cdot 3) = 12$ bars remain.

After $3$ days, $18 - (3 \cdot 3) = 9$ bars remain.

The original graph decreases by $2$ bars per day.
The new graph decreases by $3$ bars per day.

The new graph would be steeper because the number of chocolate bars decreases more quickly.