1. The problem statement, all variables and given/known data The graph shows the response of a bare thermocouple which has been subjected to a step change in temperature from 50°C to 10°C. Assuming that the bare thermocouple behaves as a single transfer lag system, determine the mathematical relationship between the temperature (T) and time (t). 2. Relevant equations To=Ti*e-(t/τ) Eq1. OR f(T)=c*e-(kt) where k= LnT1-LnT2/t1-t2 =Ln5/-20=-0.08047 Eq2. 3. The attempt at a solution Using Eq2., where t=0 : 50e-0.08047(0)=50 t=20: 50e-0.08047(20)=10 So far so good looking at the graph but for other values of time such as t=6 : 50e-0.08047(6)= 30.85, which doesn't look right on the graph. Have I got the mathematical relationship wrong? Or is my time constant wrong?