Stitz-Zeager_College_Algebra_e-book

While in the grand scheme of things both change of

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Unformatted text preview: A. y = 0 y = f (t) = et 3 t 2 −− − − − −→ −−−−−− 4 6 8 10 12 14 16 18 20 t y = T (t) 3. From the graph, we see that the horizontal asymptote is y = 70. It is worth a moment or two of our time to see how this happens analytically and to review some of the ‘number sense’ developed in Chapter 4. As t → ∞, We get T (t) = 70 + 90e−0.1t ≈ 70 + 90every big (−) . Since 1 e > 1, every big (−) = every 1 (+) ≈ very big (+) ≈ very small (+). The larger t becomes, the smaller big e−0.1t becomes, so the term 90e−0.1t ≈ very small (+). Hence, T (t) ≈ 70 + very small (+) which means the graph is approaching the horizontal line y = 70 from above. This means that as time goes by, the temperature of the coffee is cooling to 70◦ F, presumably room temperature. As we have already remarked, the graphs of f (x) = bx all pass the Horizontal Line Test. Thus the exponential functions are invertible. We now turn our attention to these inverses, the logarithmic functions, which ar...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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