Consider two identical pans containing the same amount of water that have been heated to different temperatures and then left to cool. Pan 1 was left undisturbed on the countertop, and pan 2 was left undisturbed outside. The temperature of pan 1 can be modeled by the function T (t) = 75 + 130e-0.055 where T(t) represents the temperature of the water, in degrees Fahrenheit (°F), t minutes after it starts to cool. The temperature of pan 2 can be modeled by the graph shown where T2(t) represents the temperature of the water, in degrees Fahrenheit (°F), t minutes after it starts to cool. -200 180 160 -140 420- PRIVACY 100 Temperature (degrees Fahrepheit)
Consider two identical pans containing the same amount of water that have been heated to different temperatures and then left to cool. Pan 1 was left undisturbed on the countertop, and pan 2 was left undisturbed outside. The temperature of pan 1 can be modeled by the function T (t) = 75 + 130e-0.055 where T(t) represents the temperature of the water, in degrees Fahrenheit (°F), t minutes after it starts to cool. The temperature of pan 2 can be modeled by the graph shown where T2(t) represents the temperature of the water, in degrees Fahrenheit (°F), t minutes after it starts to cool. -200 180 160 -140 420- PRIVACY 100 Temperature (degrees Fahrepheit)
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![**Graph Analysis and Question Prompt for Educational Website**
### Temperature vs Time Graph
**Description:**
The image depicts a graph illustrating the relationship between temperature and time for two different pans of water. The temperature (measured in degrees Celsius) is plotted on the vertical (Y) axis, while the time (measured in minutes) is plotted on the horizontal (X) axis.
There are two curves on the graph:
1. **Curve A (Purple Line):** This curve starts at a higher initial temperature and shows a downward slope, indicating that the temperature of the water is decreasing over time.
2. **Curve B (Blue Line):** This curve begins at a lower initial temperature compared to Curve A and similarly shows a downward slope, indicating the same trend of temperature decline over time.
Both curves eventually plateau, suggesting that the temperatures of the water in both pans stabilize after a certain period.
**Graph Information:**
- **Y-Axis Range:** 0°C to 120°C.
- **X-Axis Range:** 0 minutes to 80 minutes.
- **Curve A (Purple):** Starts near 100°C.
- **Curve B (Blue):** Starts below 80°C.
- Both curves converge around the 60-minute mark, stabilizing to a near-constant temperature.
**Question Prompt:**
**Which pan of water had a higher initial temperature? Explain your reasoning.**
**Answer Explanation:**
To determine which pan of water had the higher initial temperature, observe the starting points of each curve on the Y-axis (temperature). Curve A (Purple) begins at a temperature close to 100°C, whereas Curve B (Blue) starts below 80°C. Therefore, it is evident that the pan of water represented by Curve A had a higher initial temperature. The reasoning lies in comparing the initial values on the temperature scale, where Curve A's starting point is significantly higher than that of Curve B.
**Additional Resources:**
- [Privacy Policy]
- [Credits]
- [CA Residents: Do Not Sell My Info]
This content is designed to engage students in analyzing temperature change data, facilitating their understanding of data representation and interpretation in a real-world context.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77e1707b-64cc-476f-bf4a-b0ca9fd95e81%2Fea5cc8a7-9dd1-45f7-936e-7d33235c18b5%2F1ba64rs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Graph Analysis and Question Prompt for Educational Website**
### Temperature vs Time Graph
**Description:**
The image depicts a graph illustrating the relationship between temperature and time for two different pans of water. The temperature (measured in degrees Celsius) is plotted on the vertical (Y) axis, while the time (measured in minutes) is plotted on the horizontal (X) axis.
There are two curves on the graph:
1. **Curve A (Purple Line):** This curve starts at a higher initial temperature and shows a downward slope, indicating that the temperature of the water is decreasing over time.
2. **Curve B (Blue Line):** This curve begins at a lower initial temperature compared to Curve A and similarly shows a downward slope, indicating the same trend of temperature decline over time.
Both curves eventually plateau, suggesting that the temperatures of the water in both pans stabilize after a certain period.
**Graph Information:**
- **Y-Axis Range:** 0°C to 120°C.
- **X-Axis Range:** 0 minutes to 80 minutes.
- **Curve A (Purple):** Starts near 100°C.
- **Curve B (Blue):** Starts below 80°C.
- Both curves converge around the 60-minute mark, stabilizing to a near-constant temperature.
**Question Prompt:**
**Which pan of water had a higher initial temperature? Explain your reasoning.**
**Answer Explanation:**
To determine which pan of water had the higher initial temperature, observe the starting points of each curve on the Y-axis (temperature). Curve A (Purple) begins at a temperature close to 100°C, whereas Curve B (Blue) starts below 80°C. Therefore, it is evident that the pan of water represented by Curve A had a higher initial temperature. The reasoning lies in comparing the initial values on the temperature scale, where Curve A's starting point is significantly higher than that of Curve B.
**Additional Resources:**
- [Privacy Policy]
- [Credits]
- [CA Residents: Do Not Sell My Info]
This content is designed to engage students in analyzing temperature change data, facilitating their understanding of data representation and interpretation in a real-world context.
![**Cooling Rate of Heated Water in Pans**
Consider two identical pans containing the same amount of water that have been heated to different temperatures and then left to cool. Pan 1 was left undisturbed on the countertop, and Pan 2 was left undisturbed outside.
The temperature of Pan 1 can be modeled by the function:
\[ T_1(t) = 75 + 130e^{-0.055t} \]
where \( T_1(t) \) represents the temperature of the water, in degrees Fahrenheit (°F), \( t \) minutes after it starts to cool.
The temperature of Pan 2 can be modeled by the graph shown where \( T_2(t) \) represents the temperature of the water, in degrees Fahrenheit (°F), \( t \) minutes after it starts to cool.
**Graph Explanation:**
The graph depicts the cooling curve of Pan 2. The x-axis represents the time \( t \) in minutes after the cooling starts, and the y-axis represents the temperature \( T_2(t) \) in degrees Fahrenheit (°F).
- The temperature starts higher on the y-axis and decreases as time progresses.
- The curve demonstrates a gradual decline in temperature, indicating how the water cools over time.
The distinct decline in both models reflects the cooling behavior under different conditions (indoors vs. outdoors). The mathematical function and the graphical representation help visualize and compare the cooling rates of water in different environments.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77e1707b-64cc-476f-bf4a-b0ca9fd95e81%2Fea5cc8a7-9dd1-45f7-936e-7d33235c18b5%2Fyngci35_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Cooling Rate of Heated Water in Pans**
Consider two identical pans containing the same amount of water that have been heated to different temperatures and then left to cool. Pan 1 was left undisturbed on the countertop, and Pan 2 was left undisturbed outside.
The temperature of Pan 1 can be modeled by the function:
\[ T_1(t) = 75 + 130e^{-0.055t} \]
where \( T_1(t) \) represents the temperature of the water, in degrees Fahrenheit (°F), \( t \) minutes after it starts to cool.
The temperature of Pan 2 can be modeled by the graph shown where \( T_2(t) \) represents the temperature of the water, in degrees Fahrenheit (°F), \( t \) minutes after it starts to cool.
**Graph Explanation:**
The graph depicts the cooling curve of Pan 2. The x-axis represents the time \( t \) in minutes after the cooling starts, and the y-axis represents the temperature \( T_2(t) \) in degrees Fahrenheit (°F).
- The temperature starts higher on the y-axis and decreases as time progresses.
- The curve demonstrates a gradual decline in temperature, indicating how the water cools over time.
The distinct decline in both models reflects the cooling behavior under different conditions (indoors vs. outdoors). The mathematical function and the graphical representation help visualize and compare the cooling rates of water in different environments.
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