Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 1: Functions - Section 1.4 - Graphing with Software - Exercises 1.4 - Page 36: 42

Answer

(a) See graph. (b) $y = 6.1036x^2 - 9.2774x + 16.433$ (c) $652.92$ (d) Yes, see explanations.
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Work Step by Step

(a) We can make a scatterplot of the data as shown in the figure. (b) A regression quadratic $y = 6.1036x^2 - 9.2774x + 16.433$ can be found and superimposed on the scatterplot as shown. (c) After 11 hours, we have $y = 6.1036(11)^2 - 9.2774(11) + 16.433\approx652.92$ (d) Because the quadratic curve showed a good fit to the data set, it is expected that it would provide a good estimate of the biomass after 18 hours. However, cell growths usually follow an exponential model, thus using an exponential function for the regression will give more reliable results.
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