Calculus 8th Edition

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

Chapter 1 - Functions and Limits - 1.3 New Functions from Old Functions - 1.3 Exercises - Page 45: 62


$$(A \circ A)(x)=1.08x$$ $$(A \circ A \circ A)(x)=1.12x$$ $$(A \circ A \circ A \circ A)(x)=1.16x$$ $$( \underbrace{A \circ A \circ \cdots \circ A}_{n \text{ times}} )=(1.04)^nx$$

Work Step by Step

$$(A \circ A)(x)=A(A(x))=1.04(1.04x)=1.08x$$ $$(A \circ A \circ A)(x)=A(A(A(x)))=1.04(1.04(1.04(x)))=1.12x$$ $$(A \circ A \circ A \circ A)(x)=A(A(A(A(x))))=1.04(1.04(1.04(1.04(x))))=1.16x$$ $$( \underbrace{A \circ A \circ \cdots \circ A}_{n \text{ times}} )= \underbrace{A(A( \cdots (A}_{ n \text{ times}}(x)) \cdots ))= \underbrace{1.04(1.04( \cdots ( 1.04}_{ n \text{ times}}(x)) \cdots ))=(1.04)^nx$$
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