Concept explainers
(a)
Tofind: The recursive formula theta model the soup temperature
(a)
Answer to Problem 8P
Explanation of Solution
Given:A tureen of soup at a temperature of
. The soup cools according to the following rule, a special case of Newton’s law of cooling: Each minute, the temperature of the soup declines by 3% of the difference between the soup temperature and the room temperature.
Newton’s Law of Cooling
According to question,
Substitute the value into formula
Hence, the recursive formula is
(b)
To find: The recursive formula theta model the soup temperature
(b)
Answer to Problem 8P
Explanation of Solution
Given: A tureen of soup at a temperature of
. The soup cools according to the following rule, a special case of Newton’s law of cooling: Each minute, the temperature of the soup declines by 3% of the difference between the soup temperature and the room temperature.
Newton’s Law of Cooling
The recursive formula is
Using recursive formula to make table for 10 minutes increment from
(c)
To graph: The recursive model the soup temperature
(c)
Explanation of Solution
Given: A tureen of soup at a temperature of
. The soup cools according to the following rule, a special case of Newton’s law of cooling: Each minute, the temperature of the soup declines by 3% of the difference between the soup temperature and the room temperature.
Newton’s Law of Cooling
The recursive formula is
Using recursive formula to make table for 10 minutes increment from
Using above table and graphing utility to draw the graph.
After long term, graph is approaching the line T=70.
The temperature of soup is equal to surrounding temperature.
Chapter 12 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning