Some calc questions

A family driving across Canada in the summer experienced a delay when their motor home's engine overheated to 180C. After waiting 6 minutes in the scorching 40C heat, they checked the engine's temperature and discovered it had cooled to 160C. The engine must cool to 65"C before they can resume driving. The change in temperature of the motor home's engine follows Newton's law of cooling, represented by the exponential relationship, T - Ts = (To - T's Jekt, in which T' is the object's temperature at time , T's is the temperature of the surroundings, To is the initial temperature of the object, and & is a constant representing the relative rate of cooling of the given object. If the temperature difference between the engine and the air outside changes at a rate proportional to this temperature difference, then what is the rate of decrease of the engine's temperature at the instant when the family can get moving again? a) Step 1: State the exponential function that represents the motor home's engine temperature after time /. [2T] *Hint: solve for k b) Step 2: Determine the time f when T= 65 C. [3T] c) Step 3: Find the rate of change of the motor home's engine temperature. [3T] d) Interpret the meaning of your answer in part c), in the context of the question. [IC]