(b > 0) is known as an exponential function because the variable x appears as the exponent of the constant, or base, b. We can rule out negative values for the base to limit discussion to real numbers. Exponential functions are useful as they can be used to express proportionate rates of change in the variable y if it is measured at equal time Intervals where t measures the time interval. We can define the rate of proportionate change r in y per unit of time t by setting b =1+ r or r = b 1.

y_t=b^t

y_t/y_t-1=b

above defined a useful concept of economic and social geography, namely the rate of proportionate change r in y per unit of time t as a function of b. For a numerical illustration, calculate the rate of proportionate change r in y per unit of time t for b=1.34.