Exponential Growth and Decay

In many natural phenomena (such as population growth, radioactive decay, etc.), quantities grow or decay at a rate proportional to their size. In other words, they satisfy the following differential equation

                                                    (1)

If we call it the law of natural growth. If we call it the law of natural decay.

THEOREM: The only solution of the differential equation (1) are the exponential functions

                                                                     (2)

REMARK: It is easy to check that (2) satisfies (1). In fact,



Population Growth




Radioactive Decay




Newton's Law of Cooling




Continuous Compounded Interest