Concept explainers
For these exercises, round all estimates to one decimal place.
Another Table The following is a partial table of values for
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Use this table to complete Exercises S-21 through S-30.
Average Rate of Change Calculate the average rate of change from
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Chapter 1 Solutions
Webassign Printed Access Card For Crauder/evans/noell's Functions And Change: A Modeling Approach To College Algebra, 6th Edition, Single-term
- Using the data in Table 1 at the beginning of this section, find the average rate of change between 2005 and 2010.arrow_forwardThe American Food Dollar The following table shows the percentage P=P(d) of the American food dollar that was spent on eating away from home at restaurants, for example as function of the date d. d=Year P=Precentspentawayfromhome 1969 25 1989 30 2009 34 a. Find P(1989) and explain what it means. b. What does P(1999) mean? Estimate its value. c. What is the average rate of change per year in percentage of the food dollar spent away from home for the period from 1989 to 2009? d. What does P(2004) mean? Estimate its value. Hint: Your calculation in part c should be useful. e. Predict the value of P(2014) and explain how you made your estimate.arrow_forwardMobile Phone Sales In 2000, mobile handset sales totaled 414.99million. In 2005, the total was 778.75million. Let M=M(t) denote total mobile handset sales in year t. What was the average rate of change per year in M(t) from 2000 to 2005? Be sure to include proper units with your answer.arrow_forward
- Physician Demand The demand for physicians is expected to increase in the future, as shown in the accompanying table. Source: Association of American Medical Colleges. Year Demand for Physicians in thousands 2006 680.5 2015 758.6 2020 805.8 2025 859.3 a. Plot the data, letting t=0 correspond to 2000. Does fitting an exponential curve to the data seem reasonable? b. Use the data for 2006 and 2015, to find the function of the form f(t)=Cekt that goes through these two points. c. Use your function from part b to predict the demand for physicians in 2020 and 2025. How well do these predictions fit the data? d. If you have graphing calculator or computer program with an exponential regression feature, use it to find an exponential function that approximately fits the data. How does this answer compare with answer to part b?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_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_forward
- LIFE SCIENCE APPLICATIONS Brain Mass The brain mass of a fetus can be estimated using the total mass of the fetus by the function b=0.22m0.87, where m is the mass of the fetus in grams and b is the brain mass in grams. Suppose the brain mass of a 25-g fetus is changing at a rate of 0.25gperday. Use this to estimate the rate of change of the total mass of the fetus, dm/dt. Source: Archives dAnatomie, d Histologie et d Embryologie.arrow_forwardUse the table of values you made in part 4 of the example to find the limiting value of the average rate of change in velocity.arrow_forwardThe population of a lake of fish is modeled by the logistic equation P(t)=16,1201+25e0.75t, where t is time inyears. To the unrest hundredth, how manyyears will it take the lake to reach 80% of its carrying capacity?For the following exercises, use a graphing utility to create a scatter diagram of the data given in the table.Observe the shape of the scatter diagram to determine whether the data is best described by an exponential,logarithmic, or logistic model. Then use the appropriate regression feature to find an equation that models thedata. When necessary, round values to five decimal places.arrow_forward
- Agriculture 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_forwardFor the following exercises, use a graphing utility to create a scatter diagram of the data given in the table. Observe the shape of the scatter diagram to determine whether the data is best described by an exponential, logarithmic, or logistic model. Then use the appropriate regression feature to find an equation that models the data. When necessary, round values to ?ve decimal places.arrow_forward
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