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The temperature during a very cold day is recorded every 2 hours for 12 hours. The data are given in the table below. Time (hours) berature (903.88 6.48 9.37 10.42 8.79 4.96 0.69 Which polynomial models these data? O C(z) = 0.1672³ +2.76x² — 16.91z O C(z) = 0.003424 -0.167x³ +2.76x² - 16.91x OC(z) = 0.167³ +2.76x² - 16.91x + 38.87 OC(-0.0034x 0.167³ +2.76x² - 16.91x + 38.87

The temperature during a very cold day is recorded every 2 hours for 12 hours. The data are given in the table below. Time (hours) berature (903.88 6.48 9.37 10.42 8.79 4.96 0.69 Which polynomial models these data? O C(z) = 0.1672³ +2.76x² — 16.91z O C(z) = 0.003424 -0.167x³ +2.76x² - 16.91x OC(z) = 0.167³ +2.76x² - 16.91x + 38.87 OC(-0.0034x 0.167³ +2.76x² - 16.91x + 38.87

Advanced Engineering Mathematics
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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**Temperature Data and Polynomial Models** The temperature during a very cold day is recorded every 2 hours for 12 hours. The data are given in the table below: | Time (hours) | Temperature (°C) | |--------------|------------------| | 0 | 3.88 | | 2 | 8.48 | | 4 | 9.37 | | 6 | 10.42 | | 8 | 8.79 | | 10 | 4.96 | | 12 | 0.69 | **Which polynomial models these data?** The options given for polynomial models are: 1. \( C(t) = 0.0034t^3 - 0.167t^2 + 2.76t - 16.91 \) 2. \( C(t) = 0.167t^2 - 1.69t + 3.88 \) 3. \( C(t) = 0.167t^2 + 2.76t - 16.91 \) 4. \( C(t) = 0.0034t^3 + 2.76t^2 - 1.69t + 3.88 \) 5. \( C(t) = 0.167t^2 - 16.91t \) Each polynomial equation is a candidate model that could potentially fit the observed temperature data recorded throughout the day, using powers of \( t \) (time). **Note:** The correct model should accurately represent the trend and pattern of the data points given in the table. To determine which model best fits the data, one might plot the given temperatures and test each polynomial equation against these points.
Transcribed Image Text:**Temperature Data and Polynomial Models** The temperature during a very cold day is recorded every 2 hours for 12 hours. The data are given in the table below: | Time (hours) | Temperature (°C) | |--------------|------------------| | 0 | 3.88 | | 2 | 8.48 | | 4 | 9.37 | | 6 | 10.42 | | 8 | 8.79 | | 10 | 4.96 | | 12 | 0.69 | **Which polynomial models these data?** The options given for polynomial models are: 1. \( C(t) = 0.0034t^3 - 0.167t^2 + 2.76t - 16.91 \) 2. \( C(t) = 0.167t^2 - 1.69t + 3.88 \) 3. \( C(t) = 0.167t^2 + 2.76t - 16.91 \) 4. \( C(t) = 0.0034t^3 + 2.76t^2 - 1.69t + 3.88 \) 5. \( C(t) = 0.167t^2 - 16.91t \) Each polynomial equation is a candidate model that could potentially fit the observed temperature data recorded throughout the day, using powers of \( t \) (time). **Note:** The correct model should accurately represent the trend and pattern of the data points given in the table. To determine which model best fits the data, one might plot the given temperatures and test each polynomial equation against these points.
**Temperature Change Over Time** The table below illustrates the change in temperature over a period of 18 hours. It provides a detailed look at how temperature fluctuates hourly. | Time (hours) | 6 | 8 | 10 | 12 | 14 | 16 | 18 | |--------------|-----|-----|-----|------|-----|-----|-----| | Temperature (°C)| 3.88 | 6.48 | 9.37 | 10.42 | 8.79 | 4.96 | 0.69 | **Analysis:** - The temperature starts at 3.88°C at the 6-hour mark. - It steadily increases, reaching a peak of 10.42°C at 12 hours. - After 12 hours, the temperature begins to drop, falling to 0.69°C at 18 hours. This data can be useful for understanding daily temperature patterns and for planning weather-dependent activities.
Transcribed Image Text:**Temperature Change Over Time** The table below illustrates the change in temperature over a period of 18 hours. It provides a detailed look at how temperature fluctuates hourly. | Time (hours) | 6 | 8 | 10 | 12 | 14 | 16 | 18 | |--------------|-----|-----|-----|------|-----|-----|-----| | Temperature (°C)| 3.88 | 6.48 | 9.37 | 10.42 | 8.79 | 4.96 | 0.69 | **Analysis:** - The temperature starts at 3.88°C at the 6-hour mark. - It steadily increases, reaching a peak of 10.42°C at 12 hours. - After 12 hours, the temperature begins to drop, falling to 0.69°C at 18 hours. This data can be useful for understanding daily temperature patterns and for planning weather-dependent activities.
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