Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 7 Exponential and Logarithmic Functions - 7.7 Write and Apply Exponential and Power Functions - 7.7 Exercises - Skill Practice - Page 534: 20


$y=0.214\cdot x^{2.389}$

Work Step by Step

Let $y=ax^b$. Then our equations are: $10=a5^b$ and $81=a12^b$. If we divide the second equation by the first one we get: $8.1=2.4^b\\b=\ln_{2.4}{8.1}\approx2.389$. Then $10=a5^{2.389}\\a=\frac{10}{5^{2.389}}\approx0.214$. Thus $y=0.214\cdot x^{2.389}$
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