Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 5 - Exponential Functions - 5.2 Solving Equations Using Exponent Rules - 5.2 Exercises: 96

Answer

$h \approx ±3.50$

Work Step by Step

1. Power equation For example: $7^{x} + 3 = 0$ is an exponential equation. (The variable is the exponent.) $x^{7} + 3 =0 $ is a power equation. (The variable is raised to the power of a number.) 2. Solve $\frac{23.5h^{4}-75}{56} = 61.63$ $23.5h^{4} - 75 = 3451.28$ $23.5h^{4} = 3451.28 + 75$ $23.5h^{4} = 3526.28$ $h^{4} = 150.0544...$ $h = ±(150.0544...)^{\frac{1}{4}}$ $h = ±3.4999...$ $h \approx ±3.50$ Check: When $h = 3.4999...$ $ \frac{23.5(3.499...)^{4}-75}{56}$ $= \frac{23.5(150.0544...)-75}{56}$ $= \frac{3526.28-75}{56}$ $= \frac{3451.28}{56}$ $= 61.63$ When $h = -3.4999...$ $ \frac{23.5(-3.499...)^{4}-75}{56}$ $= \frac{23.5(150.0544...)-75}{56}$ $= \frac{3526.28-75}{56}$ $= \frac{3451.28}{56}$ $= 61.63$
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