A temperature measuring device with a time constant of 0.15 s outputs a voltage that is linearly proportional to temperature. The device is used to measure an input signal of the form T(t) = 115 + 12 sin 2t, in °C. Plot the input signal and the predicted output signal as functions of time, assuming the sensor reasonably modeled as a first-order system and the static sensitivity if 5 mV/°C. Determine the dynamic error and time lag.