SOLUTION: Suppose that a cup of hot coffee at a temperature of T0 is set down to cool in a room where the temperature is kept at T1. Then the temperature of the coffee as it cools can be mod

Question 1043870: Suppose that a cup of hot coffee at a temperature of T0 is set down to cool in a room where the temperature is kept at T1. Then the temperature of the coffee as it cools can be modeled by the function . Here, f(t) = (T0 - T1)ekt + T1 is the temperature of the coffee after t minutes; t=0 corresponds to the initial instant when the temperature of the coffee is T0; and k is a (negative) constant that depends, among other factors, on the dimensions of the cup and the material from which it is constructed. [We get this formula in calculus and is based on Newton's law of cooling.] Here are the two problems I want to discuss this week.
Problem A: Suppose that a cup of hot coffee at a temperature of 185�F is set down to cool in a room where the temperature is kept at 70F�. What is the temperature of the coffee ten minutes later? Use k = -0.15
Problem B: Suppose that a cup of hot coffee at a temperature of 185�F is set down to cool in a room where the temperature is kept at 70�F. How long will it take for the coffee to cool to 140�F?
Answer by advanced_Learner(501) (Show Source): You can put this solution on YOUR website!
Suppose that a cup of hot coffee at a temperature of T0 is set down to cool in a room where the temperature is kept at T1. Then the temperature of the coffee as it cools can be modeled by the function . Here, f(t) = (T0 - T1)ekt + T1 is the temperature of the coffee after t minutes; t=0 corresponds to the initial instant when the temperature of the coffee is T0; and k is a (negative) constant that depends, among other factors, on the dimensions of the cup and the material from which it is constructed. [We get this formula in calculus and is based on Newton's law of cooling.] Here are the two problems I want to discuss this week.
Problem A: Suppose that a cup of hot coffee at a temperature of 185�F is set down to cool in a room where the temperature is kept at 70F�. What is the temperature of the coffee ten minutes later? Use k = -0.15
Problem B: Suppose that a cup of hot coffee at a temperature of 185�F is set down to cool in a room where the temperature is kept at 70�F. How long will it take for the coffee to cool to 140�F

a.
T0=185,T1=70,K=-0.15,t=time=10 min,
Modelling equation is

find t=10
=
=
=
=
=
=
This means that when time is min the temperature is which has cooled from 185.

=
=
=
=
=
=
Take Ln of both sides
=
=

=
=
=
=

time is
it will 3.3 mins to cool to 140.
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