Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 12 - Section 12.1 - Sequences and Summation Notation - 12.1 Exercises - Page 852: 84

Answer

(a) $C_n=1.1C_{n-1}=(1.1)^n C_0$ (b) $7.09$ g/L

Work Step by Step

(a) Step 1. The initial concentration is $C_0=4$ g/L, Step 2. With an increase of $10\%$, the concentration of the first day is $C_1=1.1C_0$, Step 3. Similarly, the concentration of the second day is given by $C_2=1.1C_1$ ... ... Step 4. The concentration of the $n$th day is then given by $C_n=1.1C_{n-1}=(1.1)^n C_0$ (b) After 8 days, let $n=8$, we have $C_8=1.1C_7= ... =7.09$ g/L as shown in the figure where the concentrations up to 12 days are calculated.
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