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.

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, , , and after 2 minutes, . Plugging in these values, we get:

To find , we can set up the equation using the known temperature at :

Solving for gives us the complete equation.

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?