Answer:
67
Step-by-step explanation:
A = 25, T(0) = 100, T(1) = 90, find T(4)
dT/dt = -k(T - A)
d(T - A)/dt = -k(T - A)
d(T - A)/(T - A) = -k dt
ln(T - A) = lnC - kt
[tex]T(t) -A=Ce^{-kt}\\T(t) = A + Ce^{-kt} = 25 + Ce^{-kt}\\T(0) = 25 + C = 100\\C=75[/tex]
[tex]T(t) = 25 + 75e^{-kt}\\T(1) = 25 + 75e^{-k} = 90\\75e^{-k} = 65\\e^{-k} = \frac{65}{75}, k = ln\frac{75}{65} = 0.1431\\T(t) = 25+75e^{-0.1431t}\\T(4) = 25+75e^{-0.1431\times4} = 67.3[/tex]
