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Newton's Law of Cooling can be used to predict the temperature of a cooling liquid in a room that is at a certain steady temperature. We are going to model the temperature of cooling cup of coffee. The Fahrenheit temperature of a cup of coffee, T, in a room that is at 72 degrees Fahrenheit is given as a function of the number of minutes, m, it has been cooling by: T(m)=114(0.86)^m+72


(A) Find T(0) and, using proper units, give a physical interpretation of your answer.


(B) What does the coefficient of 114 represent in terms of the situation being modeled?


(C) By what percent does the difference between the temperature of the coffee and the temperature of the room decrease each minute?


(D) I like my coffee when it is a nice temperature of around 100 degrees Fahrenheit. How long should I wait.

Respuesta :

raphealnwobi

The temperature of the coffee when placed in the room is 114 degrees.

Exponential function

An exponential function is in the form:

y = abˣ

where y,x are variables, a is the initial value of y and b is the multiplier.

Let T represent the temperature of coffee after m minutes. Since:

[tex]T = 114(0.86)^{m}[/tex]

a) [tex]T (0)= 114(0.86)^{0}=114[/tex]

B) This means that the temperature of the coffee when placed in the room is 114 degrees.

c) The temperature degrees by 14 degrees each minute (1 - 0.86).

D)

[tex]100=114(0.86)^m\\\\m = 0.9 minutes[/tex]

The temperature of the coffee when placed in the room is 114 degrees.

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