College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 8, Sequences and Series - Chapter 8 Review - Exercises - Page 640: 31

Answer

$12,288$ bacteria

Work Step by Step

The problem can be modeled using a geometric sequence. Let $\{a_n\}$ the number of bacteria after $n-1$ sets of $5$ seconds. The elements of the sequence are: $$\begin{cases} a_1=3\\ r=2. \end{cases}$$ The $n$th term is $$a_n=a_1r^{n-1}=3(2^{n-1}).$$ In one minute there are $60/5=12$ sets of $5$ seconds. The number of bacteria after one minute is $a_{13}$: $$a_{13}=3(2^{12})=12,288.$$
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