Algebraic Modeling. **Determine Which Data Sets are Linear or Exponential**To analyze the following data sets, you need to determine whether they exhibit a linear or exponential pattern. For linear sets, calculate the slope, and for exponential sets, determine the growth factor or decay factor.**a. Data Set**- Values: - $ x $: -2, -1, 0, 1, 2, 3, 4 - Values: 1/9, 1/3, 1, 3, 9, 27, 81- Task: Choose between "linear" or "exponential" using a dropdown menu.**b. Data Set**- Values: - $ x $: -2, -1, 0, 1, 2, 3, 4 - Values: 2.2, 2.6, 3.2, 3.8, 4.4, 5.0, 5.6- Task: Choose between "linear" or "exponential" using a dropdown menu. Enter the slope or growth/decay factor in the provided space.**c. Data Set**- Values: - $ x $: -2, -1, 0, 1, 2, 3, 4 - Values: (Values not provided)- Task: Choose between "linear" or "exponential" using a dropdown menu.**Instructions**- Use the dropdown menus to select whether each data set is linear or exponential.- For linear data sets, calculate and input the slope in the provided space.- For exponential data sets, calculate and input the growth or decay factor.By understanding these characteristics, students can better grasp how datasets evolve over time, which is crucial for interpreting real-world data and trends. ### Educational Content: Analyzing Data Sets#### Data Set AnalysisIn the exercises below, you will determine the characteristics of two different data sets by identifying whether they represent a growth or decay factor or describe a slope.---#### Data Set c**Table:**```x | -2 | -1 | 0 | 1 | 2 | 3 | 4 y | 3 | 5 | 7 | 9 | 11 | 13 | 15 ```- **Analysis Question:** - This data set is [Choose: a growth factor, a decay factor, a slope] with [Fill in the blank] of [Blank].---#### Data Set d**Table:**```x | -2 | -1 | 0 | 1 | 2 | 3 | 4 y | 5.25 | 2.1 | 0.84 | 0.336 | 0.1344 | 0.05376 | 0.021504```- **Analysis Question:** - This data set is [Choose: a growth factor, a decay factor, a slope] with [Fill in the blank] of [Blank].**Options for Selection:**- a growth factor- a decay factor- a slopeMake sure to consider the x and y values to decide whether they illustrate a pattern of growth, decay, or provide the slope of a line.

Part (a) Given data set is∵y1y0=31=3 and y3y2=279=3 Hence given data set is exponential. Since y is increasing, so model is growth model. Growth factor=3 Part (b) Given data set is∵y1-y0=0.6 and y2-y1=0.6 Hence data set is linear. Slope=y1-y01-0=3.8-3.21=0.6Part (c) Given data set is∵y1-y0=2 and y2-y1=2 Hence data set is linear. Slope=y1-y01-0=9-71=2Part (d) Given data set is∵y1y0=0.3360.84=0.4 and y2y1=0.13440.336=0.4 Hence given data set is exponential. Since y is decreasing, so model is decay model. Decay factor=0.4

Math

Algebra

Determine which of the following data sets are linear and which are exponential. For the linear sets, determine the slope. For the exponential sets, determine the growth factor or the decay factor. a. This data set is -2 - 1 with 1 9 | 27 81 9 linear b. This data set is exponential 2 2.6 3.2 3.8 4.4 5.0 5.6 with

Determine which of the following data sets are linear and which are exponential. For the linear sets, determine the slope. For the exponential sets, determine the growth factor or the decay factor. a. This data set is -2 - 1 with 1 9 | 27 81 9 linear b. This data set is exponential 2 2.6 3.2 3.8 4.4 5.0 5.6 with

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Algebraic Modeling.

**Determine Which Data Sets are Linear or Exponential**

To analyze the following data sets, you need to determine whether they exhibit a linear or exponential pattern. For linear sets, calculate the slope, and for exponential sets, determine the growth factor or decay factor.

**a. Data Set**
- Values:
- $ x $: -2, -1, 0, 1, 2, 3, 4
- Values: 1/9, 1/3, 1, 3, 9, 27, 81
- Task: Choose between "linear" or "exponential" using a dropdown menu.

**b. Data Set**
- Values:
- $ x $: -2, -1, 0, 1, 2, 3, 4
- Values: 2.2, 2.6, 3.2, 3.8, 4.4, 5.0, 5.6
- Task: Choose between "linear" or "exponential" using a dropdown menu. Enter the slope or growth/decay factor in the provided space.

**c. Data Set**
- Values:
- $ x $: -2, -1, 0, 1, 2, 3, 4
- Values: (Values not provided)
- Task: Choose between "linear" or "exponential" using a dropdown menu.

**Instructions**
- Use the dropdown menus to select whether each data set is linear or exponential.
- For linear data sets, calculate and input the slope in the provided space.
- For exponential data sets, calculate and input the growth or decay factor.

By understanding these characteristics, students can better grasp how datasets evolve over time, which is crucial for interpreting real-world data and trends.

### Educational Content: Analyzing Data Sets

#### Data Set Analysis

In the exercises below, you will determine the characteristics of two different data sets by identifying whether they represent a growth or decay factor or describe a slope.

---

#### Data Set c

**Table:**
```
x | -2 | -1 | 0 | 1 | 2 | 3 | 4
y | 3 | 5 | 7 | 9 | 11 | 13 | 15
```

- **Analysis Question:**
- This data set is [Choose: a growth factor, a decay factor, a slope] with [Fill in the blank] of [Blank].

---

#### Data Set d

**Table:**
```
x | -2 | -1 | 0 | 1 | 2 | 3 | 4
y | 5.25 | 2.1 | 0.84 | 0.336 | 0.1344 | 0.05376 | 0.021504
```

- **Analysis Question:**
- This data set is [Choose: a growth factor, a decay factor, a slope] with [Fill in the blank] of [Blank].

**Options for Selection:**
- a growth factor
- a decay factor
- a slope

Make sure to consider the x and y values to decide whether they illustrate a pattern of growth, decay, or provide the slope of a line.

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