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Stitz-Zeager_College_Algebra_e-book

# Find a process for which composition with itself

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Unformatted text preview: in. 2. Assuming P and V do vary inversely, use the data to approximate the constant of proportionality. 3. Use your calculator to determine a ‘Power Regression’ to this data5 and use it verify your results in 1 and 2. Solution. k 1. If P really does vary inversely with V , then P = V for some constant k . From the data plot, k the points do seem to like along a curve like y = x . k 2. To determine the constant of proportionality, we note that from P = V , we get k = P V . Multiplying each of the volume numbers times each of the pressure numbers,6 we produce a number which is always approximately 1400. We suspect that P = 1400 . Graphing y = 1400 V x along with the data gives us good reason to believe our hypotheses that P and V are, in fact, inversely related. The graph of the data 5 6 The data with y = 1400 x We will talk more about this in the coming chapters. You can use tell the calculator to do this algebra on the lists and save yourself some time. 4.3 Rational Inequalities and Applications 275 3. After performing a ‘Power Regression’, the calculator ﬁts the data to the curve y = axb where a ≈ 1400 and b ≈ −1 with a correlation coeﬃcient which is darned near perfect7 . In other words, y = 1400x−1 or y = 1400 , as we guessed. x 7 We will revisit this example once we have developed logarithms in Chapter 6 to see how we can actually ‘linearize’ this data and do a linear regression to obtain the same result. 276 4.3.2 Rational Functions Exe...
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