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Unformatted text preview: ona , C is a measure of how
much room there is to grow given by
and k > 0 is the constant of proportionality which satisﬁes the equation
(instantaneous rate of change of N (t) at time t) = k N (t) (L − N (t))
a That is, as t → ∞, N (t) → L The logistic function is used not only to model the growth of organisms, but is also often used to
model the spread of disease and rumors.13
Example 6.5.5. The number of people N , in hundreds, at a local community college who have
heard the rumor ‘Carl is afraid of Virginia Woolf’ can be modeled using the logistic equation
N (t) = 84
1 + 2799e−t where t ≥ 0 is the number of days after April 1, 2009.
13 at which point it would be more toast than roast.
Which can be just as damaging as diseases. 6.5 Applications of Exponential and Logarithmic Functions 385 1. Find and interpret N (0).
2. Find and interpret the end behavior of N (t).
3. How long until 4200 people have heard the rumor?
4. Check your answers to 2 and 3 using...
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