**Elimination of Caffeine from the Body**The two primary ways that chemicals are eliminated from the body are through filtration by the kidneys and metabolism by enzymes from the liver. Our bodies eliminate caffeine primarily via the functioning of the kidneys. The kidneys tend to filter out a constant proportion of a chemical, that proportion depending on the particular chemical and individual.Recall that we can predict/estimate things by creating mathematical models. What type of model do you think would be best to estimate the elimination of caffeine from the body? Circle one of the following and explain your reasoning:- Linear- Quadratic- Cubic- Quartic- Exponential- Logarithmic---**Assume a person starts the day by drinking 3 cups of coffee containing 130 mg of caffeine each. How much caffeine did the person just consume?**The time it takes for the amount of a substance present to be reduced by half is called the half-life of the substance. This term is applied in many situations, including the elimination of drugs from the body and the decay of radioactive materials. For caffeine, the half-life is about 5 hours.a. Find an exponential decay function of the form $ Q(t) = Q_0 e^{-kt} $ for a person who just had 390 mg of caffeine. Hint: Plug in the information and solve for $ k $.b. How much of the original 390 mg of caffeine is in the body after 5 hours?c. Rounding to the nearest hour, when will the caffeine be reduced to the minimum amount that should no longer have any stimulant effect on the body? (Refer to the reading to determine what this amount typically is.)

Given Q(t)=Q0e-kta) To find the value of k, Half life-time to decay half of initial amountQ02=Q0e-kt12⇒12=e-5k⇒k=ln25 =0.1386 b) To find the amount left in body after 5 hours, Given half life=5 hoursSo 5 hours, half amount is leftThat is 3902=195 mgHence 195 mg left in body after 5 hours.c) To find the minimum amount, Minimum amount in body⇒as time tends to ∞Therefore Q(∞)=limt→∞Q0e-kt =0Assuming 1% caffene is safe⇒no longer have stimulant effects⇒0.01Q0=Q0e-kt⇒t=ln(100)0.1386 =33.23Hence after 33.22 hrs, minimum amount presents

Math

Calculus

Elimination of caffeine from the body The two primary ways that chemicals are eliminated from the body are through filtration by the kidneys and metabolism by enzymes from the liver. Our bodies eliminate caffeine primarily by the functioning of the kidneys. The kidneys tend to filter out a constant proportion of a chemical, that proportion depending on the particular chemical and individual. Recall that we can predict/estimate things by creating mathematical models. What type of model do you think would be best to estimate the elimination of caffeine from the body? Circle one of the following and explain your reasoning. Linear Quadratic Cubic po QuarticWE Exponential (Logarithmic eirubryba Vw od un e vol o INISS be nenala a s adt b

Elimination of caffeine from the body The two primary ways that chemicals are eliminated from the body are through filtration by the kidneys and metabolism by enzymes from the liver. Our bodies eliminate caffeine primarily by the functioning of the kidneys. The kidneys tend to filter out a constant proportion of a chemical, that proportion depending on the particular chemical and individual. Recall that we can predict/estimate things by creating mathematical models. What type of model do you think would be best to estimate the elimination of caffeine from the body? Circle one of the following and explain your reasoning. Linear Quadratic Cubic po QuarticWE Exponential (Logarithmic eirubryba Vw od un e vol o INISS be nenala a s adt b

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Directions: Construct a Regression Model for the following data. Year Wage (in dollars) 2000 5.15 2005 5.15 2010 7.25 2016 7.25 U.S. Federal Minimum Wage 1. State your regression model (least-squares line). Make sure you first convert the Year into Years after 2000. y = 2. Use your model to predict the minimum wage for the year 2022. y = dollars 3. Use your model to predict when the minimum wage will reach $10. When During year Rounding: If you do round the numbers in your work, make sure you do it during your last step.
The table below show data that has been collected from different fields from various farms in a certain valley. The table contains the grams of Raspberries tested and the amount of their Vitamin C content in mg. Find a linear model that express Vitamin C content as a function of the weight of the Raspberries. grams Vitamin C content in mg 55 11.9 60 13.7 65 15.9 70 18.5 75 20.8 80 23 85 25.8 A) Find the regression equation: places y= + Round your answers to 3 decimal B) Answer the following questions using your un-rounded regression equation. If we test 115 grams of raspberries what is the expected Vitamin C content? nearest tenth) mg (round to the
Accounting The following information is available regarding the total repair costs of Comfort Designs Company for six months of 2022: Month Units Produced Repair costs January 1,500 14,875 February 1,750 15,500 March 1,000 12,250 April 1,250 16,250 May 1,875 18,250 June 2,250 21,750 Using the least-square regression analysis on Excel, construct a cost formula. Run a regression analysis on the data above and provide your response to the following three questions. SHOW WORK (1) Provide the regression output and construct a cost model. (2) According to the cost model, what is the estimated total fixed cost? (3) According to the cost model, what is the estimated variable cost per unit?
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Amazon Revenue The annual revenue of Amazon is given in the table below (source ). Year 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 Amazon Annual Revenue (Billions of US dollars) 386.064 280.522 232.887 177.866 135.987 107.006 88.988 74.452 61.093 48.077 34.204 See the Regression page in the Chapter 1: Linear Equations and Graphs module for details on creating a regression model. Apply linear regression to the data in the table to find a model y = mx + b, where y is Amazon's annual revenue in billions of US dollars, and is the number of years since 2010.
Age l 20 25 30 35 52 67 _______________l_____________________________ Blood Pressure l 73 77 80 82 87 90 Draw a scatter diagram for the data and find the regression line.
The table shows per capita peach consumption.t Per Capita Consumption of Peaches (pounds) 1 2 Additional Materials eBook 3 4 5 6 Price (above $1.50 per pound) 0.10 0.20 0.30 4.8 4.7 6.2 6.1 7.0 6.9 7.6 7.5 8.0 8.0 8.4 8.3 8.3 0.00 5.0 4.9 6.4 6.3 7.2 7.1 7.8 7.7 8.2 8.1 8.6 8.5 (a) Find the function of the logarithmic cross-sectional model that gives per capita consumption of peaches at a price of $1.60 per pound, where f represents yearly family income in tens of thousands of dollars, with data from 1 ≤ f≤ 6. (Round all numerical values to three decimal places.) c(0.10, f) = 0.50 4.6 6.0 6.8 7.4 7.4 7.9 7.8 8.2 lb 0.40 4.7 6.1 6.9 (b) Calculate per capita peach consumption for families with a yearly income of $25,000 when the price is $1.60 per pound. (Round your answer to one decimal place.) lb
Statistics students in Oxnard College sampled 9 textbooks in the Condor bookstore and recorded the number of pages in each textbook and its cost. The data are shown below: Number of Pages (x ) Cost(y ) 720 121.6 436 75.68 363 63.19 346 65.98 325 62.25 488 93.44 980 152.4 442 67.46 262 62.06 A student calculates a linear model using technology (Statistics Calculator or Computer)ˆy = x + . (Please show your answers to two decimal places)Use the model to estimate the cost when number of pages is 274.Cost = $ (Use the linear model with yor rounded coefficients and then round your answer to 2 decimal places.)
162 Exercise The weight of 8 children were measured before and after treatment with certain drug are presented in following table .The research Question is : The weight of children beforetreatment is different from After treatmenta = 0.05 163 Id child 1 2 3 7 before treatment 32 16 37 32 44 28 27 48 After treatment 38 10 30 36 50 20 18 38
Statistics students in Oxnard College sampled 9 textbooks in the Condor bookstore and the recorded number of pages in each textbook and its cost. The data is shown below: Number of pages (x) Cost (y) 850 77.5 288 34.92 762 80.58 698 61.82 955 82.95 571 51.39 547 57.23 434 50.06 430 35.7 A student calculates a linear model using technology y = ______ x + _______.…
Statistics students in Oxnard College sampled 11 textbooks in the Condor bookstore and recorded the number of pages in each textbook and its cost. The data are shown below: Number of Pages (x)223923293366793287549761455453632 Cost(y)25.395.328.343.690.335.769.982.160.542.365.2 a. A student calculates a linear model using technology (Statistics Calculator or Computer)ˆy = x+ . (Please show your answers to two decimal places) b. Use the model to estimate the cost when number of pages is 892.Cost = $ (Use the linear model with yor rounded coefficients and then round your answer to 2 decimal places.)