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A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 66°C, it is cooling at a rate of 1°C per minute. After how many minutes does this occur?

A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 66°C, it is cooling at a rate of 1°C per minute. After how many minutes does this occur?

Calculus: Early Transcendentals
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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**Coffee Cooling Problem Explanation** **Text:** A freshly brewed cup of coffee has a temperature of 95°C in a 20°C room. When its temperature is 66°C, it is cooling at a rate of 1°C per minute. After how many minutes does this occur? **Solution:** 1. **Identify Initial and Final Temperatures:** - Initial Temperature of Coffee: 95°C - Room Temperature: 20°C - Final Temperature of Coffee when cooling rate is given: 66°C 2. **Given Cooling Rate:** - The cooling rate is 1°C per minute. 3. **Calculate the Change in Temperature:** - Temperature Change = Initial Temperature - Final Temperature - Temperature Change = 95°C - 66°C = 29°C 4. **Determine Time Taken for Cooling:** - Since the coffee is cooling at a rate of 1°C per minute: - Time = Temperature Change / Cooling Rate - Time = 29°C / 1°C per minute = 29 minutes **Conclusion:** It takes 29 minutes for the temperature of the coffee to decrease from 95°C to 66°C at a cooling rate of 1°C per minute.
Transcribed Image Text:**Coffee Cooling Problem Explanation** **Text:** A freshly brewed cup of coffee has a temperature of 95°C in a 20°C room. When its temperature is 66°C, it is cooling at a rate of 1°C per minute. After how many minutes does this occur? **Solution:** 1. **Identify Initial and Final Temperatures:** - Initial Temperature of Coffee: 95°C - Room Temperature: 20°C - Final Temperature of Coffee when cooling rate is given: 66°C 2. **Given Cooling Rate:** - The cooling rate is 1°C per minute. 3. **Calculate the Change in Temperature:** - Temperature Change = Initial Temperature - Final Temperature - Temperature Change = 95°C - 66°C = 29°C 4. **Determine Time Taken for Cooling:** - Since the coffee is cooling at a rate of 1°C per minute: - Time = Temperature Change / Cooling Rate - Time = 29°C / 1°C per minute = 29 minutes **Conclusion:** It takes 29 minutes for the temperature of the coffee to decrease from 95°C to 66°C at a cooling rate of 1°C per minute.
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