The cooling rate for three different materials is shown in the accompanying figure. The...

The cooling rate for three different materials is shown in the accompanying figure. The mathematical equation describing the cooling rate for each material is of the exponential form T(t ) = T_initiale^-at. In this relationship, T(t ) is the temperature of material at time t and the coefficient a represents the thermal capacity and resistance of the material. Determine the initial temperature and the a coefficient for each material. Which material cools the fastest, and what is the corresponding a value?