← a. Find a power function that models the data. b. Find a linear function that models the data. c. Visually determine which function is the better fit for the data. *** X 1 2 3 4 21 y 5 SSRS 9 13 39 45 5 32 6 45 0 Lond a. The power function is y = (Use integers or decimals for any numbers in the expression. Round to the nearest thousandth as needed.) b. The linear function is y=x+() (Use integers or decimals for any numbers in the expression. Round to the nearest thousandth as needed.) c. Which model is a better fit? OA. The power function is a better fit because the y-values appear to be increasing more rapidly as x increases.
← a. Find a power function that models the data. b. Find a linear function that models the data. c. Visually determine which function is the better fit for the data. *** X 1 2 3 4 21 y 5 SSRS 9 13 39 45 5 32 6 45 0 Lond a. The power function is y = (Use integers or decimals for any numbers in the expression. Round to the nearest thousandth as needed.) b. The linear function is y=x+() (Use integers or decimals for any numbers in the expression. Round to the nearest thousandth as needed.) c. Which model is a better fit? OA. The power function is a better fit because the y-values appear to be increasing more rapidly as x increases.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The image presents a question regarding which mathematical model is a better fit based on the behavior of y-values as x-values increase. The options given are:
c. Which model is a better fit?
- **A.** The power function is a better fit because the y-values appear to be increasing more rapidly as x increases.
- **B.** The linear function is a better fit because the y-values appear to be increasing more rapidly as x increases.
- **C.** The linear function is a better fit because the y-values appear to be increasing at a slower pace as x increases.
- **D.** The power function is a better fit because the y-values appear to be increasing at a slower pace as x increases.
There are no graphs or diagrams directly described in the image. The options suggest evaluating the rate of increase of the y-values to determine the suitable model fit, either a power or a linear function.
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**Title:** Modeling Data with Functions
**Objective:**
- a. Find a power function that models the data.
- b. Find a linear function that models the data.
- c. Visually determine which function is the better fit for the data.
**Data Table:**
| x | y |
|---|----|
| 1 | 5 |
| 2 | 9 |
| 3 | 13 |
| 4 | 21 |
| 5 | 32 |
| 6 | 45 |
**Instructions:**
**a. Power Function:**
- Determine a power function in the form \( y = ax^b \).
- Use integers or decimals in the expression as needed.
- Round to the nearest thousandth.
\[ \text{The power function is } y = \_\_ x^{\_\_} \]
**b. Linear Function:**
- Determine a linear function in the form \( y = mx + c \).
- Use integers or decimals in the expression as needed.
- Round to the nearest thousandth.
\[ \text{The linear function is } y = \_\_ x + (\_\_) \]
**c. Model Fit:**
- Determine which model is a better fit for the data based on visual examination.
- Choose the option that better represents the increasing y-values as x increases.
**Answer Options:**
- ○ A. The power function is a better fit because the y-values appear to be increasing more rapidly as x increases.
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F556745e6-02d3-4800-a933-7dc40a753d9d%2F7e37ca95-1011-424b-9fee-61e01040ee20%2F87z3yvv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
**Title:** Modeling Data with Functions
**Objective:**
- a. Find a power function that models the data.
- b. Find a linear function that models the data.
- c. Visually determine which function is the better fit for the data.
**Data Table:**
| x | y |
|---|----|
| 1 | 5 |
| 2 | 9 |
| 3 | 13 |
| 4 | 21 |
| 5 | 32 |
| 6 | 45 |
**Instructions:**
**a. Power Function:**
- Determine a power function in the form \( y = ax^b \).
- Use integers or decimals in the expression as needed.
- Round to the nearest thousandth.
\[ \text{The power function is } y = \_\_ x^{\_\_} \]
**b. Linear Function:**
- Determine a linear function in the form \( y = mx + c \).
- Use integers or decimals in the expression as needed.
- Round to the nearest thousandth.
\[ \text{The linear function is } y = \_\_ x + (\_\_) \]
**c. Model Fit:**
- Determine which model is a better fit for the data based on visual examination.
- Choose the option that better represents the increasing y-values as x increases.
**Answer Options:**
- ○ A. The power function is a better fit because the y-values appear to be increasing more rapidly as x increases.
---
Expert Solution
Step 1
(a) Let us take the power function of the form y = axb
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