16 Oct 2021
Problem 41
Page 143
Section 2.6: Derivatives and Rates of Change
Chapter 2: Limits and Derivatives
Textbook ExpertVerified Tutor
16 Oct 2021
Given information
To sketch a graph of the temperature of the warm soda can placed in a refrigerator as a function of time.
Step-by-step explanation
Step 1.
- The newton’s law of cooling states that the rate of decrease in temperature of the body that implies rate of cooling of a body is directly proportional to the difference in the temperature of the body at an instant of time and the temperature of the surrounding that is where is the temperature of the body at any instant of time and is the surrounding temperature.
- Let the constant of proportionality be
- Therefore, the equation can be written as
- Now solve the differential equation to find the relationship between and
- Let the initial temperature of the soda can be . That implies when ,
- Substitute this initial condition in the equation (1) to find the value of .
- Substitute the value of in the equation (1).