Math / Algebra

QuestionExample Compare the rates of change for these two functions. Which function has a greater rate of change?
Sarah's Savings $\frac{\text { vertical change }}{\text { horizontal change }}=\frac{6}{1}=6$
Alyssa's Savings
Alyssa's rate of change is greater than Sarah's.
1 What do the rates of change in the example represent? The speed that they go up $\frac{\text { vertical change }}{\text { horizontal change }}=\frac{8}{1}=8$

Studdy Solution

STEP 1

1. We are comparing the rates of change of two functions: Sarah's Savings and Alyssa's Savings.
2. The rate of change is calculated as the ratio of vertical change to horizontal change.
3. The rate of change represents how quickly the savings increase.

STEP 2

1. Understand the concept of rate of change.
2. Identify the given rates of change for Sarah's and Alyssa's savings.
3. Compare the rates of change.
4. Determine which function has a greater rate of change.

STEP 3

Understand the concept of rate of change:
The rate of change is a measure of how much one quantity changes with respect to another. In this context, it represents how quickly savings increase over time. It is calculated as the ratio of vertical change (change in savings) to horizontal change (change in time).

STEP 4

Identify the given rates of change:
For Sarah's Savings, the rate of change is given as:
$\frac{\text{vertical change}}{\text{horizontal change}} = \frac{6}{1} = 6$
For Alyssa's Savings, the rate of change is given as:
$\frac{\text{vertical change}}{\text{horizontal change}} = \frac{8}{1} = 8$

STEP 5

Compare the rates of change:
Sarah's rate of change is $6$ , while Alyssa's rate of change is $8$ .

STEP 6

Determine which function has a greater rate of change:
Since $8 > 6$ , Alyssa's rate of change is greater than Sarah's.
The function representing Alyssa's Savings has a greater rate of change.

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Studdy Solution

STEP 1

1. We are comparing the rates of change of two functions: Sarah's Savings and Alyssa's Savings.
2. The rate of change is calculated as the ratio of vertical change to horizontal change.
3. The rate of change represents how quickly the savings increase.

STEP 2

1. Understand the concept of rate of change.
2. Identify the given rates of change for Sarah's and Alyssa's savings.
3. Compare the rates of change.
4. Determine which function has a greater rate of change.

STEP 3

STEP 4

Identify the given rates of change:
For Sarah's Savings, the rate of change is given as:
$\frac{\text{vertical change}}{\text{horizontal change}} = \frac{6}{1} = 6$
For Alyssa's Savings, the rate of change is given as:
$\frac{\text{vertical change}}{\text{horizontal change}} = \frac{8}{1} = 8$

STEP 5

Compare the rates of change:
Sarah's rate of change is $6$ , while Alyssa's rate of change is $8$ .

STEP 6

Determine which function has a greater rate of change:
Since $8 > 6$ , Alyssa's rate of change is greater than Sarah's.
The function representing Alyssa's Savings has a greater rate of change.

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Studdy Solution

STEP 1

1. We are comparing the rates of change of two functions: Sarah's Savings and Alyssa's Savings.2. The rate of change is calculated as the ratio of vertical change to horizontal change.3. The rate of change represents how quickly the savings increase.

STEP 2

1. Understand the concept of rate of change.2. Identify the given rates of change for Sarah's and Alyssa's savings.3. Compare the rates of change.4. Determine which function has a greater rate of change.

STEP 3

STEP 4

STEP 5

Compare the rates of change:Sarah's rate of change is 666, while Alyssa's rate of change is 888.

STEP 6

Determine which function has a greater rate of change:Since 8>68 > 68>6, Alyssa's rate of change is greater than Sarah's. The function representing Alyssa's Savings has a greater rate of change.

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

1. We are comparing the rates of change of two functions: Sarah's Savings and Alyssa's Savings.
2. The rate of change is calculated as the ratio of vertical change to horizontal change.
3. The rate of change represents how quickly the savings increase.

1. Understand the concept of rate of change.
2. Identify the given rates of change for Sarah's and Alyssa's savings.
3. Compare the rates of change.
4. Determine which function has a greater rate of change.

Compare the rates of change:
Sarah's rate of change is $6$ , while Alyssa's rate of change is $8$ .

Determine which function has a greater rate of change:
Since $8 > 6$ , Alyssa's rate of change is greater than Sarah's.
The function representing Alyssa's Savings has a greater rate of change.