The phrase "y is proportional to x" implies that y is related to x via the equat...

The phrase "y is proportional to x" implies that y is related to x via the equation y = kx, where k is a constant. In a similar manner, "y is proportional to the square of x" implies ,"y is proportional to the product of x and z" implies y = kxz, and "y is inversely proportional to the cube of f implies . For example, when Newton proposed that the force of attraction of one body on another is proportional to the

product of the masses and inversely proportional to the square of the distance between them, we can immediately write

where G is the constant of proportionality, usually known as the universal gravitational constant. In Exercise, use these ideas to model each application with a differential equation. All rates are assumed to be with respect to time.

A potato that has been cooking for some time is removed from a heated oven. The room temperature of the kitchen is 65°F. The rate at which the potato cools is proportional to the difference between the room temperature and the temperature of the potato.