In the manufacturing of ball bearings, the components, such as the ball, are hardened through a process of heating and then rapid cooling or "quenching" by submersion in an oil or water bath. The temperature of the ball as a function of time, T(t), in the bath may be estimated as:
T(t) = (T; - ToJe-^{t}^{l}^{t} + T~
where t is the time in seconds in the bath; T; is the initial ball temperature; T~ is the oil temperature; and t is the time constant in seconds and depends upon the material of the ball, the geometry of the ball, and oil properties. Write a MATLAB function that utilizes T;; T~; t ; and three separate times, t, as input arguments and returns the ball temperature for the three times as a one-dimensional array.
Assuming an initial ball temperature of 1000°C, an oil temperature of 60°C, and the time contant t = 60 s, determine the ball temperature for times of 1, l O, and 100 seconds.