Caffeine occurs naturally in a variety of food products such as coffee, tea, and chocolate. The kidneys filter the blood and remove caffeine and other drugs through urine. The biological half-life of caffeine is approximately 6 hours. If one cup of coffee has 80 mg of caffeine, then the amount of caffeine C (in mg) remaining after t hours is given by C= 80(2)] -t/6 (a) How long will it take for the amount of caffeine to drop below 70 mig? Round to 1 decimal place. (b) Laura has trouble sleeping if she has more than 50 mg of caffeine in her bloodstream. How many hours before going to bed should she stop drinking coffee? Round to 1 decimal place, if necessary.

Plants convert carbon dioxide (CO₂) in the atmosphere, along with water and energy from sunlight, into the energy they need for growth and reproduction. Experiments were performed under normal atmospheric air conditions and in air with enriched CO₂ concen- trations to determine the effect on plant growth. The plants were given the same amount of water and light for a four-week period. The following table gives the plant growths in grams: Normal Air: 4.67 4.21 2.18 3.91 4.09 5.24 2.94 4.71 4.04 5.79 3.80 4.38 Enriched Air: 5.04 4.52 6.18 7.01 4.36 1.81 6.22 5.70 On the basis of these data, we want to determine the effect of CO2-enriched atmosphere on plant growth. Let X be the plant growth in enriched air and Y be the plant growth in normal air. Assume X, Y are normal with mean x, y respectively, but we don't know their variances. µx (i) Construct a 95% (two-sided) confidence interval for px - y by discarding the last four data from the larger sample and then pair up the rest of the two…

An important tool in archeological research is radiocarbon dating, developed by the American chemist Willard F. Libby.3 This is a means of determining the age of certain wood and plant remains, and hence of animal or human bones or artifacts found buried at the same levels. Radiocarbon dating is based on the fact that some wood or plant remains contain residual amounts of carbon-14, a radioactive isotope of carbon. This isotope is accumulated during the lifetime of the plant and begins to decay at its death. Since the half-life of carbon-14 is long (approximately 5730 years),4 measurable amounts of carbon-14 remain after many thousands of years. If even a tiny fraction of the original amount of carbon-14 is still present, then by appropriate laboratory measurements the proportion of the original amount of carbon-14 that remains can be accurately determined. In other words, if Q(t) is the amount of carbon-14 at time t and Q0 is the original amount, then the ratio Q(t)/Q0 can be…

Medical studies of obesity use the Body Mass Index (BMI), which is defined by w BMI = where w is weight in kilograms and h is height in meters. (a) Using the fact that 1 kg = 2.2 lb and 1 meter = 39.4", calculate the BMI of a 5'5" woman who weighs 150 lb. (b) Which has more effect on the BMI: a 10% weight increase or a 10% height decrease? Justify your answer.