Newton's Law of Cooling

Suppose a very hot object is placed in a cooler room.[br]Or suppose a very cool object is placed inside a much hotter room. [br][br][color=#0000ff][b]Newton's Law of Cooling[/b][/color] states that the [b]rate of change of temperature of an object[/b] is [b]directly proportional[/b] [b]to the [br][br]DIFFERENCE BETWEEN the[br][/b][b][color=#ff0000]current temperature of the object [/color][/b][b]& the[br][/b][color=#980000][b]initial temperature of the object. [br][br][/b][/color]In differential equations, this is written as [math]\frac{dT}{dt}=k\left(T-R\right)[/math], where [br][br][b][color=#ff0000][i]T[/i] = the current temperature of the object,[/color][/b][br][color=#0000ff][b][i]R[/i] = the temperature of the surrounding medium (room),[/b][/color] & [br][i]k[/i] = some constant of proportionality (a value for which you'll often have to solve). [br][br][b][color=#1e84cc]Calculus Students:[/color][/b][br]You can use this applet as a reference in checking your solution to any differential equation you solve that relates to Newton's Law of Cooling. (The function appears in the upper left-hand corner.) [br][br][b][color=#1e84cc]PreCalculus & Calculus Students:[/color][br][/b]You can use this applet as a reference to check your work in solving application problems that relate to evaluating exponential functions and/or solving exponential equations within this context. You can enter the following information on the right side: [br][br][b][color=#980000]Initial Temperature of the Object[/color][/b][br][b]One Data Point: (n, temperature after n minutes)[/b][br][br]After doing so, you can enter in any [color=#9900ff][b]time value[/b][/color] or [color=#ff0000][b]temperature value[/b][/color] and interpret the meaning of the other coordinate in the corresponding point that appears in the graph on the left.
HOTTER OBJECT entering a COOLER ROOM
COOLER OBJECT entering a HOTTER ROOM
Quick (Silent) Illustrator

Information: Newton's Law of Cooling