Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
Kleiber’s law states that for the vast majority of animals, the metabolic rate
a. The Eastern gray squirrel weighs about
b. How does a
c. Based on your answer to part b, would overeating ( the same amount for each ) be more likely to lead to weight gain for the man or for the woman?
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- 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?arrow_forwardStopping Distance The table below shows the average stopping distance D, in feet, for a car on dry pavement versus the speed S of the car, in miles per hour. S= speed mph 15 25 35 40 60 75 D = stopping distance feet 44 85 136 164 304 433 a Find a model of stopping distance as power function of speed. b If speed is doubled, how is stopping distance affected? c Plot the data and the power model on the same screen.arrow_forwardIs it Proportional? In Exercises S17 through S25, determine whether or not the relationship described is a proportionality relationship. A Mans Height Is a mans height proportional to his age?arrow_forward
- Mortgage 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_forwardThe Decibel scale Exercise S-7 through S-10 refer to the decibel scale. If one sound has a relative intensity one-tenth that of another, how do their decibel levels compare?arrow_forwardImmigration The following graph shows immigrationin thousand to the United States has varied over the past century. Source: Homeland Security. a. Find the average annual rate of change in immigration for the first half of the century from 1905 to 1955. b. Find the average annual rate of change in immigration for the second half of the century from 1955 to 2005. c. Find the average annual rate of change in immigration for the entire century from 1905 to 2005. d. Average your answers to part a and b, and compare the result with your answer from part c. Will these always be equal for any two time periods? e. If the annual average rate of change for entire century continues, predict the number of immigrants in 2009. Compare answer to the actual number of 1,130,818 immigrants.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_forwardArctic Foxes The age-weight relationship of female Arctic foxes caught in Svalbard, Norway, can be estimated by the function Mt=3102e-e-0.022t-56, where t is the age of the fox in days and Mt is the weight of the fox in grams. Source: Journal of Mammalogy. a. Estimate the weight of a female fox that is 200 days old. b. Use Mt to estimate the largest size that a female fox can attain. Hint: Find limtMt. c. Estimate the age of a female fox when it has reached 80% of its maximum weight. d. Estimate the rate of change in weight of an Arctic fox that is 200 days old. Hint: Recall that Dteft=f'teft. e. Using a graphing calculator to graph Mt and then describe the growth pattern. f. Use the table function on a graphing calculator or a spreadsheet to develop a chart that shows the estimated weight and growth rate of female foxes for days 50,100,150,200,250, and 300.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
- The Kelvin Temperature Scale Physicists and chemists often use the Kelvin temperature scale. In order to determine the relationship between the Fahrenheit and Kelvin temperature scales, a lab assistant put Fahrenheit and Kelvin thermometers side by side and took readings at various temperatures. The following data were recorded. K = kelvins F = degrees Fahrenheit 200 -99.67 220 -63.67 240 -27.67 260 8.33 280 44.33 300 80.33 a. Show that the temperature F in degrees Fahrenheit is a linear function of the temperature K in kelvins. b. What is the slope of this linear function? Note: Be sure to take into account that the table lists kelvins in jumps of 20 rather than in jumps of 1. c. Find a formula for the linear function. d. Normal body temperature is 98.6 degrees Fahrenheit. What is that temperature in kelvins? e. If temperature increases by 1 kelvin, by how many degrees Fahrenheit does it increase? If temperature increases by 1 degree Fahrenheit, by how many kelvins does it increase? f. The temperature of 0 kelvins is known as absolute zero. It is not quite accurate to say that all molecular motion ceases at absolute zero, but at that temperature the system has its minimum possible total energy. It is thought that absolute zero cannot be attained experimentally, although temperatures lower than 0.0000001 kelvin have been attained. Find the temperature of absolute zero in degrees Fahrenheit.arrow_forwardLIFE SCIENCE APPLICATIONS Metabolic Rate The average daily metabolic rate for rodents can be expressed as a function of weight by m=85.65w0.54, where w is the weight of the rodent in kg and m is the metabolic rate in kcal/day. Source: Wildlife Feeding and Nutrition. a. Suppose that the weight of the rodent is changing with respect to time at a rate dw/dt. Find dm/dt. b. Determine dm/dt for a 0.25-kg rodent that is gaining weight at a rate of 0.01kg/day.arrow_forward
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