SOLUTION: Use Newton's Law of Cooling, T=C+(Tsubscript0 - C)e^kt to solve the below:
A pizza removed from the oven has a temperature of 450 degrees Fahrenheit. It is left sitting on a room
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Question 1161289: Use Newton's Law of Cooling, T=C+(Tsubscript0 - C)e^kt to solve the below:
A pizza removed from the oven has a temperature of 450 degrees Fahrenheit. It is left sitting on a room that has a temperature of 70 degrees Fahrenheit. After 5 minutes, the temperature of the pizza is 315 degrees Fahrenheit.
a. Use Newton's Law to find the model for the temperature of the pizza T, after t minutes.
answer: 315 = 70 + (5mins - 450)e^kt
b. What is the temperature of the pizza after 25 minutes?
answer - ???
c. When will the temperature of the pizza be 130 degrees Fahrenheit?
answer: ???
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
I bake frozen pizzas for my husband very often, so I can figure this out.
=temperature at time
=temperature at time
=ambient temperature
The units we use for and for the temperatures do not matter as long as we are consistent.
At makes
As approaches ,
needs to approach ,
so that approaches ,
so the constant must be a negative number.
a. With time in minutes and temperature in degrees Fahrenheit,
the data gives us the equation ,
or , if we simplify.
We need to find , and substitute its value into
to find the model
(a formula we can use to figure out how long to wait for that pizza to cool).
I could use (or a rounded version of that) in the next equation, but I will let the calculator remember the number and keep crunching numbers.
According to my scientific calculator,
} (rounded to 4 significant figures).
So, the model is
b. After 25 minutes ,
so we substitute that value into our model to find for that pizza.
From experience, I say we waited too long.
Using rounded values, ,so
, and continuing to round, ,
so
After 25 minutes, the temperature of the pizza is .
c. To find out when the temperature of the pizza will be
(in degrees Fahrenheit), we substitute that into our model, getting
as the equation to solve.
and according to my calculator, .
So, according to our model, to eat the pizza at , we have to wait .
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