Modelling Drug ConcentrationA drug trial is studying the efficacy of a new drug for thalassemia, a genetic disorder in which a patient isunable to properly synthesize the hemoglobin molecule in the blood. In the trial, the rate at which thedrug is metabolized by the body is studied. The data from the trial is then used to construct a model forthe drug's metabolism. The concentration of a drug, f(t) in parts per million, in a patient's blood thours after the drug is administered is given by the functionf(t) = -t5 + 3t* – 6t3 – 2t? + 60tThe goal of this tutorial is to graph this function and analyze and interpret the graph within the problemcontext.Show the following steps on the blackboard or paper as your instructor directs:d) Use the procedure for sketching polynomial functions (p. 189) to sketch the graph for f(t). Showclearly all steps of this procedure.e) Identify the practical domain on your graph and state the practical domain in interval notation.f) Using your graph, estimate when the drug attains maximum concentration. Check your answer byusing graphing software (graphing calculator, wolframalpha phone app or website, desmos.com, etc).

Given: ft=-t5+3t4-6t3-2t2+60t Note: Since the procedure is missing, we have used the standard…

Answered: A drug trial is studying the efficacy…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.6: Variation

Problem 31E

See similar textbooks

Similar questions

Logistic Population growth the table and scatter plot give the population of black flies in a closed laboratory container over an 18 day period. (a) Use the logistic command on your calculator to find a logistic model for these data. (b) Use the model to estimate the time when there were 400 flies in the container
Weight Versus Height The following data show the height h, in inches, and weight w, in pounds, of an average adult male. h 61 62 66 68 70 72 74 75 w 131 133 143 149 155 162 170 175 a Make a power model for weight versus height. b According to the model from part a, what percentage increase in weight can be expected if height is increased by 10?
Long-Term Data and the Carrying Capacity This is a continuation of Exercise 13. Ideally, logistic data grow toward the carrying capacity but never go beyond this limiting value. The following table shows additional data on paramecium cells. t 12 13 14 15 16 17 18 19 20 N 610 513 593 557 560 522 565 517 500 a. Add these data to the graph in part b of Exercise 13. b. Comment on the relationship of the data to the carrying capacity. Paramecium Cells The following table is adapted from a paramecium culture experiment conducted by Cause in 1934. The data show the paramecium population N as a function of time t in days. T 2 3 5 6 8 9 10 11 N 14 34 94 189 330 416 507 580 a. Use regression to find a logistic model for this population. b. Make a graph of the model you found in part a. c. According to the model you made in part a, when would the population reach 450?
Sales of a video game released in the year 2000 took off at first, but then steadily slowed as time moved on. Table 4 shows the number of games sold, in thousands, from the years 20002010. a. Let x represent time in years starting with x=1 for the year 2000. Let y represent the number of games sold in thousands. Use logarithmic regression to fit a model to these data. b. If games continue to sell at this rate, how many games will sell in 2015? Round to the nearest thousand.
Richter Scale Exercise S-1 through S-6 use elementary properties of Richter Scale. If the Richter scale reading of one quake is t units larger than that of a second quake, how do the relative intensities of the quake compare?
Eastern Pacific Yellowfin Tuna Studies to fit a logistic model to the Eastern Pacific yellowfin tuna population have yielded N=1481+36e2.61t where t is measured in years and N is measured in thousands of tons of fish. a. What is the r value for the Eastern Pacific yellowfin tuna? b. What is the carrying capacity K for the Eastern Pacific yellowfin tuna? c. What is the optimum yield level? d. Use your calculator to graph N versus t. e. At what time was the population growing the most rapidly?
World Population The following table shows world population N, in billions, in the given year. Year 1950 1960 1970 1980 1990 2000 2010 N 2.56 3.04 3.71 4.45 5.29 6.09 6.85 a. Use regression to find a logistic model for world population. b. What r value do these data yield for humans on planet Earth? c. According to the logistic model using these data, what is the carrying capacity of planet Earth for humans? d. According to this model, when will world population reach 90 of carrying capacity? Round to the nearest year. Note: This represents a rather naive analysis of world population.

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Functions and Change: A Modeling Approach to Coll…

Algebra

ISBN:

9781337111348

Author:

Bruce Crauder, Benny Evans, Alan Noell

Publisher:

Cengage Learning

Trigonometry (MindTap Course List)

Trigonometry

ISBN:

9781337278461

Author:

Ron Larson

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Functions and Change: A Modeling Approach to Coll…

Algebra

ISBN:

9781337111348

Author:

Bruce Crauder, Benny Evans, Alan Noell

Publisher:

Cengage Learning

Trigonometry (MindTap Course List)

Trigonometry

ISBN:

9781337278461

Author:

Ron Larson

Publisher:

Cengage Learning

College Algebra

Algebra

ISBN:

9781938168383

Author:

Jay Abramson

Publisher:

OpenStax

Algebra and Trigonometry (MindTap Course List)

Algebra

ISBN:

9781305071742

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

College Algebra

Algebra

ISBN:

9781305115545

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS