It is known that a certain object has constant of proportionality k = 1/40 in Newton’s l...

It is known that a certain object has constant of proportionality k = 1/40 in Newton’s law of cooling.

When the temperature of this object is 0⁰F, it is placed in a medium whose temperature is changing in time according to

(a) Using Newton’s law of cooling, show that the temperature of the object at time t is

(b) What happens to the temperature of the object as t →+∞? Is this reasonable?

(c) Determine the time, t_max, when the temperature of the object is a maximum. Find T (t_max) and T_m(t_max).

(d) Make a sketch to depict the behavior of T (t) and T_m(t).