Researchers measured the blood alcohol concentration (BAC) of eight adult male subjects after rapid consumption of 30 mL of ethanol (corresponding to two standard alcoholic drinks). The table shows the data they obtained by averaging the BAC (in g/mL) of the eight men.
(a) Use the readings to sketch the graph of the BAC as a function of t
(b) Use your graph to describe how the effect of alcohol varies with time.
t (hours) | BAC |
0 | 0 |
0.2 | 0.025 |
0.5 | 0.041 |
0.75 | 0.040 |
1.0 | 0.033 |
1.25 | 0.029 |
1.5 | 0.024 |
1.75 | 0.022 |
2.0 | 0.018 |
2.25 | 0.015 |
2.5 | 0.012 |
3.0 | 0.007 |
3.5 | 0.003 |
4.0 | 0.001 |
Source: Adapted from P. Wilkinson et.al., “Pharmacokinetics of Ethanol after Oral Administration in the Fasting State,” Journal of Pharmacokinetics and Biopharmaceutics 5(1977): 207–24.
Want to see the full answer?
Check out a sample textbook solutionChapter 1 Solutions
Bundle: Calculus, 8th + Enhanced WebAssign - Start Smart Guide for Students + WebAssign Printed Access Card for Stewart's Calculus, 8th Edition, Multi-Term
- Can the average rate of change of a function be constant?arrow_forwardTable 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?arrow_forwardA driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 3:40 p.m. At this time, he started pumping gas into the tank. At exactly 3:44, the tank was full and he noticed that he had pumped 10.7 gallons. What is the average rate of flow of the gasoline into the gas tank?arrow_forward
- Does a linear, exponential, or logarithmic model best fit the data in Table 2? Find the model.arrow_forwardTable 2 shows a recent graduate’s credit card balance each month after graduation. a. Use exponential regression to fit a model to these data. b. If spending continues at this rate, what will the graduate’s credit card debt be one year after graduating?arrow_forwardWhat does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?arrow_forward
- Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.arrow_forwardEnter the data from Table 2 into a graphing calculator and graph the ranking scatter plot. Determine whetherthe data from the table would likely represent a function that is linear, exponential, or logarithmic.arrow_forwardIf you travel 100 miles in two hours, then your average speed for the trip is Average speed=_________=________arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage