It will take approximatelyhour(s) for the amount of caffeine to drop below 70 mg. 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 drugsthrough 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)-/6(a) How long will it take for the amount of caffeine to drop below 70 mg? 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.

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Answered: Caffeine occurs naturally in a variety…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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.
the half life of caffeine in a healthy adult's bloodstream in 5.7 hours. suppose alex, a healthy adult, drinka a grande latte, which contains 150mg of caffeine, at 4pm. use the exponential decay model where t is the time since 4 pm measured in hours, k is exponential decay rate of caffeine and a9t) is the amount of caffeine in alex's bloodstream at time t
4.) (For Marketing & Sales Analysts-Consultants). Four months after the deliveries of goods were affected by the granular lockdown due to the Covid-19 pandemic, a manufacturer noticed that sales had dropped from 100,000 units per month to 80,000 units. If the sales follow an exponential pattern decline, what will they be after another 4 months? Note: Use the exponential model, y= Cekt, where t is measured in months.
6. From 1790 to 1860, U.S. population grew rapidly (see the table). Let f(t) be the population t years after 1790. a) Create a scattergram for the data on your Graphing Calculator. b) Based on your scattergram, what appears more appropriate, a linear model, or an exponential model? Explain Year 1790 1800 1810 1820 1830 1840 1850 1860 d) What is the base? What does it tell us about the rate of population growth? Population (millions) 3.9 5.3 7.2 9.6 12.9 17.1 23.2 31.4 c) Use ExpReg on your GC to find an equation to model the situation. Write your answer using function notation. Round using 6 decimal places.
the sales revenue of a new mobile phone model is found to follow an AR(1) process, as shown below. what is the 3-lag AČF value? Xt =0.7*xt-1+Wt 0.700 .0.343 0.490 0.240
Inorganic phosphorous is a naturally occurring element in all plants and animals, with concentrations increasing progressively up the food chain (fruit < vegetables < cereals < nuts < corpse). Geochemical surveys take soil samples to determine phosphorous content (in ppm, parts per million). A high phosphorous content may or may not indicate an ancient burial site, food storage site, or even a garbage dump. The Hill of Tara is a very important archaeological site in Ireland. It is by legend the seat of Ireland's ancient high kings†. Independent random samples from two regions in Tara gave the following phosphorous measurements (ppm). Assume the population distributions of phosphorous are mound-shaped and symmetric for these two regions. Region I: x1; n1 = 12 540 810 790 790 340 800 890 860 820 640 970 720 Region II: x2; n2 = 16 750 870 700 810 965 350 895 850 635 955 710 890 520 650 280 993 (a) Use a calculator with mean and standard deviation keys…
Inorganic phosphorous is a naturally occurring element in all plants and animals, with concentrations increasing progressively up the food chain (fruit < vegetables < cereals < nuts < corpse). Geochemical surveys take soil samples to determine phosphorous content (in ppm, parts per million). A high phosphorous content may or may not indicate an ancient burial site, food storage site, or even a garbage dump. The Hill of Tara is a very important archaeological site in Ireland. It is by legend the seat of Ireland's ancient high kings†. Independent random samples from two regions in Tara gave the following phosphorous measurements (ppm). Assume the population distributions of phosphorous are mound-shaped and symmetric for these two regions. Region I: x1; n1 = 12 540 810 790 790 340 800 890 860 820 640 970 720 Region II: x2; n2 = 16 750 870 700 810 965 350 895 850 635 955 710 890 520 650 280 993 (a) Use a calculator with mean and standard deviation keys…

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