Answer:
After 50.4 min.
Step-by-step explanation:
Newton's law of cooling-
\(T(t)=t_a+(t_0-t_a)e^{-kt}\)
where,
\(t_0\) = the initial temp. = 200° F
k = 0.1947,
\(T(t)\) = 180° F
\(t_a\) = 67° F
Putting the values,
\(\Rightarrow 180=67+(200-67)e^{-0.1947\cdot t}\)
\(\Rightarrow 180-67=(200-67)e^{-0.1947\cdot t}\)
\(\Rightarrow (200-67)e^{-0.1947\cdot t}=180-67\)
\(\Rightarrow 133e^{-0.1947\cdot t}=113\)
\(\Rightarrow e^{-0.1947\cdot t}=\dfrac{113}{133}\)
\(\Rightarrow \ln e^{-0.1947\cdot t}=\ln \dfrac{113}{133}\)
\(\Rightarrow -0.1947\cdot t=\ln \dfrac{113}{133}\)
\(\Rightarrow t=\dfrac{\ln \dfrac{113}{133}}{-0.1947}=0.84\ h=50.4\ min\)
