Big Ideas Math - Algebra 1, A Common Core Curriculum

Published by Big Ideas Learning LLC
ISBN 10: 978-1-60840-838-2
ISBN 13: 978-1-60840-838-2

Chapter 6 - Exponential Functions and Sequences - 6.6 - Geometric Sequences - Exercises - Page 336: 33

Answer

$16$; $8$; $4$.

Work Step by Step

Number of teams remaining after a particular round is $\frac{1}{2}$ times the number of teams remaining after the previous round. This implies that the number of teams remaining after the $n$th round is $\frac{1}{2^n}a$, where $a$ is the number of teams in the beginning. In our case $a=128$. The number of teams remaining after the third round is: $\frac{1}{2^3}\times128=16$ After the fourth round: $\frac{1}{2^4}\times128=8$ After fifth round: $\frac{1}{2^5}\times128=4$
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