College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.4 - Page 492: 124

Answer

sample answer: The percentage should be lower. E.G. For $ 10\%$ risk, the blood alcohol concentration is about 0.02.

Work Step by Step

(sample answer) 17 is about one-sixth of 100. So the expentancy is that a driver with a 0.08 blood alcohol concentration will be in an accident once every six times he sits at the wheel. The odds feel dangerous, so I would prefer this to be lower, say once in TEN, which is $ 10\%$ risk. In example 9, p.487, a model is given for the risk based on blood alcohol concentration: $R=6e^{12.77x} $ which , for x=0.08 yields R=17 (percent) If we want $R=10,$ solve for x: $10=6e^{12.77x}\quad/\div 6$ $\displaystyle \frac{10}{6}=e^{12.77x}\qquad$... apply ln( ) to both sides $\displaystyle \ln\frac{10}{6}=12.77x\qquad/\div 12.77$ $ x=\displaystyle \frac{\ln\frac{10}{6}}{12.77}\approx$0.0173726507139$\approx 0.02$
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