Question
An object has been heated to 190 degrees
Fahrenheit. It is brought into a room where
the temperature is 65 degrees Fahrenheit.
After 2 minutes the temperature of the object
is down to 150 degrees. Find the equation
of the function that models the temperature
of the object as a function of time.
Fahrenheit. It is brought into a room where
the temperature is 65 degrees Fahrenheit.
After 2 minutes the temperature of the object
is down to 150 degrees. Find the equation
of the function that models the temperature
of the object as a function of time.
Ask by Whittaker Garza. in the United States
Mar 29,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The temperature of the object as a function of time is modeled by:
where
Solution
The object cools according to Newton’s Law of Cooling, which can be modeled by
Given that:
-
(initial temperature), -
(room temperature),
the model becomes
We are also given that after
Subtract
Divide both sides by
Taking the natural logarithm of both sides:
and solving for
Thus, the equation of the function is
An equivalent way to express it is by writing the exponential term in power form:
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution The Deep Dive
To model the temperature of the object as a function of time, we can use Newton’s Law of Cooling, which states that the rate of change of the temperature of an object is proportional to the difference between its temperature and the ambient temperature. The solution is generally expressed as:
In this case,
To find
Solving for
Once you have this equation, it’s a breeze to calculate the temperature at any given time! You can even use it to predict when the object will reach a certain temperature. Just remember, the earlier you catch it, the warmer it will be!
Did you know Newton’s Law of Cooling was formulated by Sir Isaac Newton in the late 17th century? While Newton is commonly recognized for his laws of motion and gravity, his work on cooling was revolutionary. It laid the groundwork for thermodynamics and understanding heat transfer, influencing fields from engineering to meteorology! Isn’t it interesting how a simple observation about warm bread cooling on a table can lead to such profound scientific understanding?
