Chapter 5

# 4 rules 1a log b b b log b 1 2 log b pq

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Unformatted text preview: igger the value of f(x) approaches    Theorem :  Let a be any real number.  The instantaneous rate of change of the  function  f ( x ) = e x at x = a is ea    So the instantaneous rate of change of the function  f ( x ) = e x  at the point  ( a ,e a ) is ea .  This property is unique to the exponential  function  f ( x ) = e x  or constant multiples of the exponential function such as  f ( x ) = ke x where k is a constant.    You will have to remember and use this theorem frequently when you take Calculus.                x Ex:   In a biology experiment, let N(t) be the number of bacteria in a colony after t  hours, where t = 0 corresponds to the time the experiment begins.  Suppose that  during the period from t = 4 hours to t = 8 hours the number of bacteria is modeled  by the experimental function N(t) = 4et :     ...
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## This note was uploaded on 02/08/2011 for the course MATH 3 taught by Professor Staff during the Winter '08 term at UCSC.

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