The Family of Exponential Functions The formula = gives a family of exponential functions with positive parameters (the initial P P0at P0 quantity) and (the base, or growth/decay factor). The base tells us whether the function is a increasing (a > 1) or decreasing (0 < < 1). Since is the factor by which changes when is a a P t increased by 1, large values of mean fast growth; values of near 0 mean fast decay. (See Figures a a and .) All members of the family = are concave up. P P0at
The Family of Exponential Functions The formula P = P0at gives a family of exponential functions with positive parameters P0 (the initial quantity) and a (the base, or growth/decay factor). The base tells us whether the function is increasing (a > 1) or decreasing (0 < a < 1). Since a is the factor by which P changes when t is increased by 1, large values of a mean fast growth; values of a near 0 mean fast decay. (See Figures and .) All members of the family P = P0at are concave up.
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