Holy Cross College, Fall Semester, 2003 Math 131, Professor Hwang Descriptions of Exponential Growth The text has three ways of describing exponential growth. While these three methods are mathematically equivalent, the book’s terminology about “rate of growth/decay” can be confusing, and demands careful attention to wording. General Base Let a > 0 be a positive constant. The general exponential function with base a is a function of the form f ( t ) = P0 a t . Usually the variable t represents time, measured in units appropriate to a given problem. The constant P0 represents the amount of “stuF” at time 0. ±or each increment of t by one unit, an exponential function’s value gets multiplied by a , because f ( t + 1) = P0 a t +1 = P0 a t · a = a · f ( t ) . Consequently, if 0 < a < 1, then f is decreasing (by a factor of a for each time unit), while if a > 1, then f is increasing (by a factor of a for each time step). Growth Rate
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This note was uploaded on 03/26/2012 for the course MAC 2312 taught by Professor Bonner during the Fall '08 term at University of Florida.