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asymptote of the graph, conﬁrming our answer to part 2, and the graph intersects the line
y = 42 at x = ln(2799) ≈ 7.937, which conﬁrms our answer to part 3. 84
y = f (x) = 1+2799e−x and
y = 84 84
y = f (x) = 1+2799e−x and
y = 42 14
Or, more likely, three people started the rumor. I’d wager Jeﬀ, Jamie, and Jason started it. So much for telling
your best friends something in conﬁdence!
15
See, for example, Example 6.1.2. 386 Exponential and Logarithmic Functions If we take the time to analyze the graph of y = N (x) above, we can see graphically how logistic
growth combines features of uninhibited and limited growth. The curve seems to rise steeply, then
at some point, begins to level oﬀ. The point at which this happens is called an inﬂection point
or is sometimes called the ‘point of diminishing returns’. At this point, even though the function is
still increasing, the rate at which it does so begins to decline. It turns out the point of diminishing
returns always occurs at half the limiting population. (In our...

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