When a cake is removed from an oven, its temperature is measured at 300◦F. Three minutes later its temperature is 200◦F. Assume the room temperature is 70◦F. How long will it take for the cake to cool...

When a cake is removed from an oven, its temperature is measured at 300
◦
F. Three minutes later its temperature is 200
◦
F. Assume the room temperature is 70
◦
F. How long will it take for the cake to cool off to 75
◦
F?

Steps: using Python

1. 
   

   
   Use the model above to set up an initial value problem and solve it. (In this step,
   k
   is a symbolic constant, you may leave it in your answer.) Print your solution in terms of
   t
   and
   k
   .
   

   
   


2. 
   

   
   Use the condition “three minutes later its temperature is 200
   ◦
   F” to find the value of
   k
   . Print out the expression for
   k
   and the solution
   T
   (
   t
   ) with this
   k
   .
   

   
   


3. 
   

   
   Answer the question: when
   T
   = 75, find the time
   t
   by the result of previous step. Print your answer and evaluate it.