Similarly as x 2 we imagine substituting 3 x 2000001

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Unformatted text preview: . Since x = −2 continues to produce a 0 in the x+2 x+4 (x+2)2 denominator of the reduced function, we know x = −2 is a vertical asymptote to the graph, which the calculator confirms. The graph of y = h(x) The graph of y = r(x) Our next example gives us a physical interpretation of a vertical asymptote. This type of model arises from a family of equations cheerily named ‘doomsday’ equations.6 The unfortunate name will make sense shortly. Example 4.1.3. A mathematical model for the population P , in thousands, of a certain species of bacteria, t days after it is introduced to an environment is given by P (t) = (5100)2 , 0 t < 5. −t 1. Find and interpret P (0). 2. When will the population reach 100,000? 6 This is a class of Calculus equations in which a population grows very rapidly. 238 Rational Functions 3. Determine the behavior of P as t → 5− . Interpret this result graphically and within the context of the problem. Solution. 1. Substituting t = 0 gives P (0) = into the environment. 100 (5−0)2 = 4, which me...
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