Examples of Output Response for step Input

This video provides the Examples of output response for a step input.
EXAMPLE:- 1
A Thermometer initially at 100C is dipped at time t=0 into an oil bar maintained at 150C. Calculate the time required for thermometer to reach a temperature of 130C.Given Data : Time Constant=1.2 minutes, Kp=1
EXAMPLE:- 2
When a thermometer at 30C is placed in a water bath at 90C , the initial rate of rise in thermometer temperature is found to be 2C/s. What is the time constant of the thermometer, assuming it is a first order device with unity steady state gain ? What will Thermometer read after 1 minute?
EXAMPLE:- 3
A heater for a semiconductor wafer has first-order dynamics that is the transfer function relating changes in temperature T to changes in the heater input power level P is
T(s)/P(s)=K/(Ts+1)
where K has units [°C/Kw] and T has units [min].
The process is at steady state when an engineer changes the power input stepwise from 1 to 1.5 Kw. She notes the following:
The process temperature initially is 80 °C.
Four minutes after changing the power input, the temperature is 230 °C.
Thirty minutes after the temperature is 280 °C.
What are K and T in the process transfer function?

[@mc.rjohns]

Which book does the third question come from?

[@Swamic2]

A thermometer requires 2 min to indicate 98% of
the response to a step input. Assuming the thermometer to
be a first-order system, find the time constant.
If the thermometer is placed in a bath, the temperature
of which is changing linearly at a rate of 10°/min, how much
error does the thermometer show?
please solve