Newton's law of cooling indicates that the temperature of a warn object will decrease exponentially with time and will approach the temperature of the

glasskerfu

glasskerfu

Answered question

2021-02-09

Newton's law of cooling indicates that the temperature of a warn object will decrease exponentially with time and will approach the temperature of the surrounding air. The temperature T(t) is modeled by T(t)=Ta+(T0Ta)ekt. In this model, Ta represents the temperature of the surrounding air, T0 represents the initial temperature of the object and t is the time after the object starts cooling. The value of k is the cooling rate and is a constant related to the physical properties the object.
A cake comes out of the oven at 335F and is placed on a cooling rack in a 70F kitchen. After checking the temperature several minutes later, it is determined that the cooling rate k is 0.050. Write a function that models the temperature T(t) of the cake t minutes after being removed from the oven.

Answer & Explanation

Macsen Nixon

Macsen Nixon

Skilled2021-02-10Added 117 answers

Given:
The initial temperature (T0 ) of the cake is 335F.
The tempearture (Ta) of the cake when place in cooling tray is 70F.
The cooling rate (k) is 0.050.
Known fact:
By the Newton's law of cooling , the temperature is modeled as
T(t)=Ta+(T0Ta)ekt
where, Ta is the temperature surronded by air.
T0 is the initial temperature
t is the time after the object starts cooling,
k is the cooling rate.
Calculation:
The function that models the temperature of the cake t minutes after being removed from the oven is computed as follows.
Substitute
T0=335F,Ta=70F and k=0.050 T(t)=Ta+(T0+Ta)ekt
T(t)=70+(33570)e(0.050)t
=70+265e(0.050)t
Answer:
The function that models the temperature of the cake t minutes after it is removed from the oven is T(t)=70+265e(0.050)t

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