Unformatted text preview: case, when y = 42.) While these
concepts are more precisely quantiﬁed using Calculus, below are two views of the graph of y = N (x),
one on the interval [0, 8], the other on [8, 15]. The former looks strikingly like uninhibited growth;
the latter like limited growth. 84
y = f (x) = 1+2799e−x for
0≤x≤8 6.5.2 84
y = f (x) = 1+2799e−x for
8 ≤ x ≤ 16 Applications of Logarithms Just as many physical phenomena can be modeled by exponential functions, the same is true of
logarithmic functions. In Exercises 6a, 6b and 6c of Section 6.1, we showed that logarithms are
useful in measuring the intensities of earthquakes (the Richter scale), sound (decibels) and acids and
bases (pH). We now present yet a diﬀerent use of the a basic logarithm function, password strength.
Example 6.5.6. The information entropy H , in bits, of a randomly generated password consisting
of L characters is given by H = L log2 (N ), where N is the number of possible symbols for each
character in the password. In general...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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