Answer: The coffee will reach a temperature of 143 degrees in 10.45 minutes
Explanation: Please see the attachments below
Applying Newton's law of cooling, the correct answer is, the coffee will cool down to a temperature of 143 degrees in 10.4 minutes.
Given that, the initial temperature of the coffee,
[tex]T_1=195^\circ F[/tex]
The temperature of the room is given to be,
[tex]T_2=60^\circ F[/tex]
Temperature after time t = 20 mins is given as,
[tex]T(t)=183^\circ F[/tex]
According to Newton's law of cooling, temperature as a function of time 't' is given by,
[tex]T(t)=T_2+(T_1-T_2)\,exp(kt)[/tex]
Now, substituting all the known values we get the value of 'k',
[tex]183^\circ F=60^\circ F + (195^\circ F - 60^\circ F)\,exp(k\times 2)[/tex]
[tex]123^\circ F= (135^\circ F)\,exp(k\times 2)\\[/tex]
[tex]\implies \frac{123^\circ F}{135^\circ F} =exp(k\times 2)[/tex]
Now applying logarithm on both sides;
[tex]ln(0.911)=2k[/tex]
[tex]\implies k=-0.0466\, min^{-1}[/tex]
Now we are asked to find the value of 't' when;
[tex]T(t)= 143^\circ F[/tex]
i.e.;
[tex]143^\circ F=60^\circ F + (195^\circ F - 60^\circ F)\,exp(-0.0466\times t)[/tex]
[tex]83^\circ F= (135^\circ F)\,exp(-0.0466\times t)[/tex]
[tex]t=\frac{1}{-0.0466}\times ln(\frac{83^\circ F}{135^\circ F} )=10.439\, minutes[/tex]
Find out more about Newton's law of cooling here:https://brainly.com/question/13748261
