PLEASE ANSWER IN AN EASY TO READ FORMAT!!!! PLEASE AND THANK YOU!!!! Make sure to answer all parts of the question. ### Analysis of Monthly High Temperatures in Atlanta for 2021The table below provides data on the high temperatures recorded in Atlanta for each month of the year 2021. Each month is associated with its corresponding high temperature in degrees Fahrenheit.| Month | Temperature (°F) ||-------|------------------|| 1 | 53 || 2 | 57 || 3 | 65 || 4 | 73 || 5 | 80 || 6 | 86 || 7 | 88 || 8 | 87 || 9 | 82 || 10 | 72 || 11 | 63 || 12 | 55 |#### Objective:Develop a trigonometric model that accurately represents the data listed above.#### Steps to Arrive at the Solution:1. **Identify Patterns in Data:** - Analyze the temperature data to recognize any cyclical and periodic patterns, typical of weather data over a year.2. **Choose the Right Trigonometric Function:** - Since temperatures tend to rise and fall periodically, consider using sinusoidal functions (sine or cosine), which naturally model periodic behavior.3. **Determine Amplitude, Frequency, Phase Shift, and Vertical Shift:** - **Amplitude (A)** represents half the range of temperature variation: \[ \text{Range} = \text{Maximum Temperature} - \text{Minimum Temperature} = 88 - 53 = 35 \] \[ A = \frac{\text{Range}}{2} = \frac{35}{2} = 17.5 \] - **Vertical Shift (D)** is the midpoint (average) of the maximum and minimum temperatures: \[ D = \frac{\text{Maximum Temperature} + \text{Minimum Temperature}}{2} = \frac{88 + 53}{2} = 70.5 \] - **Frequency (B)** is related to the period of the seasons; typically, for a year, the period is 12 months. \[ B = \frac{2\pi}{\text{Period}} = \frac{2\pi}{12} = \frac{\pi}{6

Given : MonthTemperature153257365473580686788887982107211631255To find : The table shows the high…

2. The table below shows the high temperatures for each month of 2021 in Atlanta where month 1 is January. Write a trig model that represents the data. Month 2 3 4 5 6 7 8 9 10 11 12 Temperature 53 57 65 73 80 86 88 87 82 72 63 55 Explain the steps you took to arrive at your solution.

2. The table below shows the high temperatures for each month of 2021 in Atlanta where month 1 is January. Write a trig model that represents the data. Month 2 3 4 5 6 7 8 9 10 11 12 Temperature 53 57 65 73 80 86 88 87 82 72 63 55 Explain the steps you took to arrive at your solution.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

PLEASE ANSWER IN AN EASY TO READ FORMAT!!!! PLEASE AND THANK YOU!!!! Make sure to answer all parts of the question.

### Analysis of Monthly High Temperatures in Atlanta for 2021

The table below provides data on the high temperatures recorded in Atlanta for each month of the year 2021. Each month is associated with its corresponding high temperature in degrees Fahrenheit.

| Month | Temperature (°F) |
|-------|------------------|
| 1 | 53 |
| 2 | 57 |
| 3 | 65 |
| 4 | 73 |
| 5 | 80 |
| 6 | 86 |
| 7 | 88 |
| 8 | 87 |
| 9 | 82 |
| 10 | 72 |
| 11 | 63 |
| 12 | 55 |

#### Objective:
Develop a trigonometric model that accurately represents the data listed above.

#### Steps to Arrive at the Solution:
1. **Identify Patterns in Data:**
- Analyze the temperature data to recognize any cyclical and periodic patterns, typical of weather data over a year.

2. **Choose the Right Trigonometric Function:**
- Since temperatures tend to rise and fall periodically, consider using sinusoidal functions (sine or cosine), which naturally model periodic behavior.

3. **Determine Amplitude, Frequency, Phase Shift, and Vertical Shift:**
- **Amplitude (A)** represents half the range of temperature variation:
\[
\text{Range} = \text{Maximum Temperature} - \text{Minimum Temperature} = 88 - 53 = 35
\]
\[
A = \frac{\text{Range}}{2} = \frac{35}{2} = 17.5
\]
- **Vertical Shift (D)** is the midpoint (average) of the maximum and minimum temperatures:
\[
D = \frac{\text{Maximum Temperature} + \text{Minimum Temperature}}{2} = \frac{88 + 53}{2} = 70.5
\]
- **Frequency (B)** is related to the period of the seasons; typically, for a year, the period is 12 months.
\[
B = \frac{2\pi}{\text{Period}} = \frac{2\pi}{12} = \frac{\pi}{6

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