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 - Quiz for Lessons 7.6-7.7 - Page 536: 14


$y=4.406\cdot x^{0.912}$

Work Step by Step

Let $y=ax^b$. Then our equations are: $12=a3^b$ and $36=a10^b$. If we divide the second equation by the first one we get: $3=(\frac{10}{3})^b\\b=\ln_{\frac{10}{3}}{3}\approx0.912$. Then $12=a3^{0.912}\\a=\frac{12}{3^{0.912}}\approx4.406$. Thus $y=4.406\cdot x^{0.912}$
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