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A drug response curve describes the level of medication in the bloodstream after a drug is administered. A surge function
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Chapter 6 Solutions
Single Variable Calculus
- Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?arrow_forwardThe half-life of plutonium-244 is 80,000,000 years. Find function gives the amount of carbon-14 remaining as a function of time, measured in years.arrow_forwardCan the average rate of change of a function be constant?arrow_forward
- A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 3:40 p.m. At this time, he started pumping gas into the tank. At exactly 3:44, the tank was full and he noticed that he had pumped 10.7 gallons. What is the average rate of flow of the gasoline into the gas tank?arrow_forwardCancer Insulation workers who were exposed to asbestos and employed before 1960 experienced an increased likelihood of lung cancer. If a group of insulation workers has a cumulative total of 100,000 years of work experience with their first date of employment t years ago, then the number of lung cancer causes occuring within the group can be modeled using the function Nt=0.00437t3.2. Find the rate of growth of the number of workers with lung cancer in a group as described by the following first dates of employment. Source: Observation and Inference: An Introduction to the Methods of Epidemiology. a. 5 years ago b. 10 years agoarrow_forwardbThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.arrow_forward
- Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.arrow_forwardWhat does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?arrow_forwardAgriculture Pregnant sows tethered in stalls often show high levels of repetitive behavior, such as bar biting and chain chewing, indicating chronic stress. Researchers from Great Britain have developed a function that estimates the relationship between repetitive behavior, the behavior of sows in adjacent stalls, and food allowances such that ln(T)=5.493.00ln(F)+0.18ln(C) where T is the percent of time spent in repetitive behavior, F is the amount of food given to the sow in kilograms per day, and C is the percent of time that neighboring sows spent bar biting and chain chewing. Source: Applied Animal Behaviour Science. a. Solve the above expression for T. b. Find and interpret T when F=2, and C=40.arrow_forward
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