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Solution.
84
84
3
1. We ﬁnd N (0) = 1+2799e0 = 2800 = 100 . Since N (t) measures the number of people who have
heard the rumor in hundreds, N (0) corresponds to 3 people. Since t = 0 corresponds to April
1, 2009, we may conclude that on that day, 3 people have heard the rumor.14 2. We could simply note that N (t) is written in the form of Equation 6.7, and identify L = 84.
However, to see why the answer is 84, we proceed analytically. Since the domain of N is
restricted to t ≥ 0, the only end behavior of signiﬁcance is t → ∞. As we’ve seen before,15
84
as t → ∞, have 1997e−t → 0+ and so N (t) ≈
≈ 84. Hence, as t → ∞,
1+very small (+)
N (t) → 84. This means that as time goes by, the number of people who will have heard the
rumor approaches 8400.
3. To ﬁnd how long it takes until 4200 people have heard the rumor, we set N (t) = 42. Solving
84
= 42 gives t = ln(2799) ≈ 7.937. It takes around 8 days until 4200 people have
1+2799e−t
heard the rumor.
4. We graph y = N (x) using the calculator and see that the line y = 84 is the hor...

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