Question 2

This question is related to Newton's law of cooling.

Let T(t) be the temperature of a body of liquid at time t.

Let Am be the room (ambient) temperature of the surrounding medium (air).

The DE is T' (t) = k·(Am - T(t)) where k is the cooling rate constant.

Solve the differential equation in Maple for Am = 20 degrees and an initial temperature of 50 degrees.

Given also that T(20) = 35, determine k. Now compute T(60). Do all the calculations in Maple.

Finally graph I(t) for 0 ≤ t ≤ 100 together with the room temperature on a suitable domain/range.