Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
Population Growth The following table shows the population of reindeer on an island as of the given year.
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We let
a. Approximate
b. Use your work from part
c. The number you calculated in part
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Chapter 6 Solutions
FUNCTIONS AND CHANGE COMBO
- Running Speed A man is running around a circular track that is 200 m in circumference. An observer uses a stopwatch to record the runner’s time at the each of each lap, obtaining the data in the following table. (a) What was the man’s average speed (rate) between 68 s and 152 s? (b) What was the man’s average speed between 263 s and 412 s? (c) Calculate the man’s speed for cadi lap, Is he slowing down, speeding up, or neither?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_forwardThe 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_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_forwardMolars 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_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
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