Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 11 - Further Topics in Algebra - 11.3 Geometric Sequences and Series - 11.3 Exercises: 11

Answer

$a)A_{10}=0.01\times 2^{10-1}=0,01\times 2^{9}=5.12\$ ;$ $b)S_{n}=0.01\times \left( 2^{10}-1\right) =10.23\$ $

Work Step by Step

Amount earned on the indicated day can be calculated with using simple geometric sequence formula $A_{n}=0.01\times 2^{n-1}$ And the total amount earned will be $ S_{n}=\dfrac {A_{1}\left( 1-r^{n}\right) }{1-r}=\dfrac {0.01\times \left( 1-2^{n}\right) }{1-2}=0.01\left( 2^{n}-1\right) $ $\Rightarrow a)A_{10}=0.01\times 2^{10-1}=0,01\times 2^{9}=5.12\$ ;$ $b)S_{n}=0.01\times \left( 2^{10}-1\right) =10.23\$ $
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