# 6 when will your body have eliminated all the

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6. When will your body have eliminated all the caffeine? Caffeine, like most common drugs, is classified as a first-order drug because exponential decay accurately PRGHOV LWV HOLPLQDWLRQ IURP WKH KXPDQ ERG\² \$OFRKRO´ RQ WKH RWKHU KDQG´ LV D ]HURµRUGHU GUXJ² /HW­V ORRN DW what the difference is.

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From the August 2010 issue of 8cZf_fc7<c`d`eXk`fe7IXk\7 J_\\k7) Assume that 24-year-old Bryan has been eating and drinking for most of the evening and by midnight has a blood alcohol concentration (BAC) level of 0.19 g/dl (grams/deciliter)—far above the legal driving limit of 0.08 g/dl. If Bryan weighs 140 lbs., it would take approximately seven drinks for his BAC to reach 0.19 g/dl. Fortunately for Bryan, a friend has already taken his car keys. The question now is, When should the keys be given back to Bryan? If someone were to monitor Bryan’s BAC over the next 8 hours, it would most likely look like the data in the following table. Alcohol Elimination Rate Time (hrs) Alcohol (g/dl) Time (hrs) Alcohol (g/dl) Time (hrs) Alcohol (g/dl) 0 0.190 3 0.145 6 0.100 1 0.175 4 0.130 7 0.085 2 0.160 5 0.115 8 0.070 1. Make a scatter plot of the data (time, alcohol) from the table. 2. Determine the best-fit regression equation for this graph. 3. The general form of the equation for this graph is y = ax + b . In terms of the quantities you have just graphed, explain the meaning of the constants a and b in this equation. ¸² \$V PHQWLRQHG´ %U\DQ ZLVHO\ VWRSSHG GULQNLQJ DW PLGQLJKW² /HJDOO\´ %U\DQ FDQQRW GULYH KRPH XQWLO KLV %\$& is at or below 0.08 g/dl. When will he be sober enough, legally, to drive home? Note that the 0.08 g/dl BAC OHYHO LV VWDWXWRU\ LQ DOO VWDWHV¹ KRZHYHU´ PDQ\ VWDWHV KDYH ª]HUR WROHUDQFH« ODZV IRU SHUVRQV XQGHU WKH DJH RI 21. Under these laws, drivers who are not yet 21 cannot have any alcohol in their body while driving. 5. When was all the alcohol eliminated from Bryan’s body? 6. On the calculator or on paper, shade the region that shows the no-drive zone for Bryan. Write the two inequalities that describe this region. 7. Does the term legal drive zone imply that this zone is necessarily a safe drive zone? 8. The elimination rate of alcohol from the human body is highly variable. The rate you found here is an average value, but elimination rates as low as 0.01 g/dl per hour are common. At this conservative rate, at what time would the alcohol have been eliminated from Bryan’s body? 9. What are the differences between zero-order drugs (such as alcohol) and first-order drugs (such as caffeine)? 10. Write a short reflection on this investigation, summarizing what you have learned as well as any personal reactions.
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