6 250 rational functions the denominator x2 4 would

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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 −t (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 t 4.9 4.99 4.999 4.9999 P (t) 10000 1000000 100000000 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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