Mathematics 134 – Intensive Calculus for Science 2 Quiz 9 – April 21, 2006

Your Name:

Do all work on this sheet (front and back). You have 15 minutes. Approved calculators OK on this quiz.

Newton’s Law of Cooling states that the rate at which the temperature of an object changes is proportional to the difference between the object’s temperature and the surrounding temperature.

A) (5) Express Newton’s Law of Cooling as a differential equation. Call the object’s temperature T and the surrounding temperature A (a constant).

B) (10) Solve for T from your equation in part A.

C) (10) A hot horseshoe with temperature 200^{∘}C is placed into a large vat of water maintained at constant temperature 30^{∘}C. Ten minutes later the horseshoe has cooled to 140^{∘}C. How long will it take to cool off to 75^{∘}C?