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Unformatted text preview: ans 4000 bacteria are initially introduced 2. To ﬁnd when the population reaches 100,000, we ﬁrst need to remember that P (t) is measured
in thousands. In other words, 100,000 bacteria corresponds to P (t) = 100. Substituting
for P (t) gives the equation (5100)2 = 100. Clearing denominators and dividing by 100 gives
(5 − t)2 = 1, which, after extracting square roots, produces t = 4 or t = 6. Of these two
solutions, only t = 4 in in our domain, so this is the solution we keep. Hence, it takes 4 days
for the population of bacteria to reach 100,000.
3. To determine the behavior of P as t → 5− , we can make a table
4.9999 P (t)
10000000000 In other words, as t → 5− , P (t) → ∞. Graphically, the line t = 5 is a vertical asymptote of
the graph of y = P (t). Physically, this means the population of bacteria is increasing without
bound as we near 5 days, which cannot physically happen. For this reason, t = 5 is called
the ‘doomsday’ for this population. There...
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