Concept explainers
Traffic Accidents The following table shows the cost
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The rate of vehicular involvement in traffic accidents (per vehicle-mile) can be modeled as a quadratic function of vehicular speed
a. Use regression to find a cubic model for the data. (Keep two decimal places for the regression parameters written in scientific notation.)
b. Calculate
c. At what speed is the cost of traffic accidents (for commercial vehicles driving at night on urban streets) at a minimum? (Consider speeds between
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FUNCTIONS+CHANGE -WEBASSIGN
- aThe average rate of change of a function f between x=a and x=b is the slope of the ___________ line between (a,f(a)) and (b,f(b)).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_forwardMass of Bighorn Yearlings The body mass of yearling bighorn sheep on Ram Mountain in Alberta, Canada, can be estimated by M(t)=27.5+0.3t0.001t2 Where M(t) is measured in kilograms and t is days since May 25. Source: Canadian Journal of zoology. a. Find the average rate of change of the mass of bighorn yearling between 105 and 115 days past May 25. b. Find the instantaneous rate of change of the mass for a bighorn yearling sheep whose age is 105 days past May 25. c. Graph the function M(t) on [5,125] by [25,65]. d. Does the behavior of the function past 125 days accurately model the mass of the sheep? Why or why not? e. f. g.arrow_forward
- Molars The crown length as shown below of first molars in fetuses is related to the postconception age of tooth as L(t)=0.01t2+0.788t7.048, Where L(t) is the crown length, in millimeters, of the molar t weeks after conception. Source: American Journal of Physical Anthropology. a. Find the average rate of growth in crown length during weeks 22 through 28. b. Find the instantaneous rate of growth in crown length when the tooth is exactly 22 weeks of age. c. Graph the function on [0,50] by [0,9]. Does a function that increases and then begins to decrease make sense for this particular application? What do you suppose is happening during the first 11 weeks? Does this function accurately model crown length during those weeks?arrow_forwardEstimate the age of a newly discovered fossil for which the ratio of carbon-14 to carbon-12 is R=1/1014.arrow_forwardTable 4 gives the population of a town (in thousand) from 2000 to 2008. What was the average rate of change of population (a) between 2002 and 2004, and (b) between 2002 and 2006?arrow_forward
- Population Growth and Decline The table gives the population in a small coastal community for the period 1997-2006. Figures shown arc for January 1 in each year. (a) What was the average rate of change of population between 1998 and 2001? (b) What was the average rate of change of population between 2002 and 2004? (C) For what period of lime was the population increasing? (d) For what period of time was the population decreasing?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_forwardMortgage Rates The following table is taken from the website of Freddie Mac. It shows rates for 30-year fixed-rate mortgages since 1970. y=Year r=Mortgagerate 1975 9.05 1980 13.74 1985 12.43 1990 10.13 1995 7.93 2000 8.05 2005 5.87 2010 4.69 2015 3.84 a. Explain in practical terms the meaning of r(2003). b. Use the table to estimate the value of r(2003).arrow_forward
- Body Mass Index The following graph shows how the body mass index-for-age percentile for girls varies from the age of 2to20 years. Source: Centers for Disease Control. a. Sketch a graph of the rate of change of the 95th percentile as a function of age. b. Sketch a graph of the rate of change of the 50th percentile as a function of age.arrow_forwardLIFE 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_forwardWeight 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?arrow_forward
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