Stitz-Zeager_College_Algebra_e-book

A y 2 28x 7 b x 82 64 y 9 9 c y 12

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Unformatted text preview: n(N ) = A ln(t) + ln(B ). If we set X = ln(t) and Y = ln(N ), this equation becomes Y = AX + ln(B ). In other words, we have a line with slope A and Y -intercept ln(B ). So, instead of plotting N versus t, we plot ln(N ) versus ln(t). ln(t) ln(N ) 0 0.693 1.099 1.386 1.609 1.792 1.946 2.079 2.197 2.302 2.398 2.485 2.565 4.997 5.549 5.905 6.489 6.800 6.989 7.306 7.546 7.771 7.824 8.143 8.385 8.454 ln(t) ln(N ) 2.639 8.566 2.708 2.773 2.833 2.890 2.944 2.996 8.653 8.779 8.925 9.042 9.045 9.086 Running a linear regression on the data gives The slope of the regression line is a ≈ 1.512 which corresponds to our exponent A. The y -intercept b ≈ 4.513 corresponds to ln(B ), so that B ≈ 91.201. In other words, we get the model N = 91.201t1.512 , something from Section 5.3. Of course, the calculator has a built-in ‘Power Regression’ feature. If we apply this to our original data set, we get the same model we arrived at before.19 19 Critics may question why the authors of the book have chosen to even discuss linearization of data when the calculator has a Power Regression built-in and ready to go. Our respons...
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