**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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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 + _______.…
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[Simple Linear Regression] How do you solve this?