Exponential functions, continuous growth and differential equations

This is known as an exponential function to base A. When x increases in value this function obviously increases in value very rapidly ifA is a number substantially greater than 1. On the other hand, the value of Ax approaches zero if x takes on larger and larger negative values. For all values of A it can be deduced from the general rules for exponents (explained in Chapter 2) that A0 = 1 and A1 = A.