Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - 6.2 Exponential Functions and Their Derivatives - 6.2 Exercises: 19

Answer

(a) 265 mi (b) 1084588 miles

Work Step by Step

(a) As we know 1 ft = 12 inches This implies 2 ft = 24 inches $f(24)=(24)^{2} =576$ inches This implies $f(24)=\frac{576}{12}$ ft $=48$ ft As per statement, $g(x)=2^{x}=g(24)=2^{24}$inches Hence, $g(24)=2^{24}$inches Since, $1$ mile $=5280$ ft Thus, $g(24)=\frac{2^{24}}{12\times 5280}=265$ mi (b) Since 3 ft = 36 inches Thus, $log_{2}x=36$ Using formula $log_{b}x=y=b^{y}=x$ This implies $x=2^{36}$ inches Hence, $x= \frac{2^{36}}{12\times 5280}\approx 1084588$ miles
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