**Exponential Equations: Understanding Initial Value, Common Ratio, and Growth/Decay**The table below represents an exponential equation. Your task is to determine the initial value, the common ratio (multiplier), and whether the function exhibits growth or decay.To type a fraction such as $ \frac{1}{3} $ use the forward slash like this 1/3.### Data Table:```| x | y ||-----|------|| 0 | 500 || 1 | 100 || 2 | 20 || 3 | 4 |```### Questions:1. **Initial value is**: [Input Box]2. **Common ratio (multiplier) is**: [Input Box]3. **Growth or decay?**: [Input Box] (type out either "growth" or "decay")---### Analysis:- **Initial Value**: This is the value of $ y $ when $ x = 0 $. From the table, when $ x = 0 $, $ y = 500 $.- **Common Ratio (Multiplier)**: This is the factor by which the value of $ y $ changes as $ x $ increases by 1. You can find the common ratio by dividing any $ y $ value by the previous $ y $ value. For example: - $ \frac{100}{500} = 0.2 $ - $ \frac{20}{100} = 0.2 $ - $ \frac{4}{20} = 0.2 $The common ratio is 0.2.- **Growth or Decay**: If the common ratio is less than 1, the function represents decay. If it is greater than 1, the function represents growth. Since the common ratio here is 0.2 (which is less than 1), this function represents decay.### Final Input Values:- Initial value is: 500- Common ratio (multiplier) is: 0.2- Growth or decay?: decay---**Educational Note**: Understanding exponential equations is crucial in various fields such as biology, finance, and physics. In real-world scenarios, exponential growth describes processes that increase rapidly over time, while exponential decay describes processes that decrease rapidly over

Exponential function are functions which increase or decrease in fixed proportion. They have a…

The table below represents an exponential equation. Find the initial value, the common ratio (multiplier), and whether it.is growth or decay. To type a fraction such as use the forward slash like this 1/3. y 500 100 20 3 4 Initial value is Common ratio (multiplier) is Growth or decay? (type out either "growth" or "decay")

The table below represents an exponential equation. Find the initial value, the common ratio (multiplier), and whether it.is growth or decay. To type a fraction such as use the forward slash like this 1/3. y 500 100 20 3 4 Initial value is Common ratio (multiplier) is Growth or decay? (type out either "growth" or "decay")

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

**Exponential Equations: Understanding Initial Value, Common Ratio, and Growth/Decay**

The table below represents an exponential equation. Your task is to determine the initial value, the common ratio (multiplier), and whether the function exhibits growth or decay.

To type a fraction such as $ \frac{1}{3} $ use the forward slash like this 1/3.

### Data Table:
```
| x | y |
|-----|------|
| 0 | 500 |
| 1 | 100 |
| 2 | 20 |
| 3 | 4 |
```

### Questions:
1. **Initial value is**: [Input Box]
2. **Common ratio (multiplier) is**: [Input Box]
3. **Growth or decay?**: [Input Box] (type out either "growth" or "decay")

---

### Analysis:

- **Initial Value**: This is the value of $ y $ when $ x = 0 $. From the table, when $ x = 0 $, $ y = 500 $.

- **Common Ratio (Multiplier)**: This is the factor by which the value of $ y $ changes as $ x $ increases by 1. You can find the common ratio by dividing any $ y $ value by the previous $ y $ value. For example:
- $ \frac{100}{500} = 0.2 $
- $ \frac{20}{100} = 0.2 $
- $ \frac{4}{20} = 0.2 $

The common ratio is 0.2.

- **Growth or Decay**: If the common ratio is less than 1, the function represents decay. If it is greater than 1, the function represents growth. Since the common ratio here is 0.2 (which is less than 1), this function represents decay.

### Final Input Values:

- Initial value is: 500
- Common ratio (multiplier) is: 0.2
- Growth or decay?: decay

---

**Educational Note**: Understanding exponential equations is crucial in various fields such as biology, finance, and physics. In real-world scenarios, exponential growth describes processes that increase rapidly over time, while exponential decay describes processes that decrease rapidly over

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