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Hwang exponential

# Hwang exponential - Holy Cross College Fall Semester 2003...

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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 ) = P 0 a t . Usually the variable t represents time, measured in units appropriate to a given problem. The constant P 0 represents the amount of “stuff” at time 0. For each increment of t by one unit, an exponential function’s value gets multiplied by a , because f ( t + 1) = P 0 a t +1 = P 0 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 When a population grows at a rate of 2 . 6% per year, the number of individuals
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