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Final Exam Schedule – Fall, 2014 11:00 ClassThursday, December 1110:30 – 12:30 2:00 ClassThursday, December 111:00 – 3:00 3:30 ClassTuesday, December 93:30.

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Presentation on theme: "Final Exam Schedule – Fall, 2014 11:00 ClassThursday, December 1110:30 – 12:30 2:00 ClassThursday, December 111:00 – 3:00 3:30 ClassTuesday, December 93:30."— Presentation transcript:

1 Final Exam Schedule – Fall, 2014 11:00 ClassThursday, December 1110:30 – 12:30 2:00 ClassThursday, December 111:00 – 3:00 3:30 ClassTuesday, December 93:30 – 5:30

2 Planet Average Distance from the Sun (in millions of km) Time to Make Complete Orbit (in days) Mercury57.988 Venus108.2225 Earth149.6365 Mars228.0687 Jupiter778.64333 Saturn1427.410760 Uranus2838.230686 Neptune4497.860191 Pluto5913.590739 123456789123456789

3 Planet Average Distance from the Sun (in millions of km) Time to Make Complete Orbit (in days) Mercury57.988 Venus108.2225 Earth149.6365 Mars228.0687 Jupiter778.64333 Saturn1427.410760 Uranus2838.230686 Neptune4497.860191 Pluto5913.590739

4 Planet Average Distance from the Sun (in millions of km) Time to Make Complete Orbit (in days) Mercury57.988 Venus108.2225 Earth149.6365 Mars228.0687 Jupiter778.64333 Saturn1427.410760 Uranus2838.230686 Neptune4497.860191 Pluto5913.590739 Make a scatter plot of time of orbit versus distance from the sun.

5 Planet Average Distance from the Sun (in millions of km) Time to Make Complete Orbit (in days) Mercury57.988 Venus108.2225 Earth149.6365 Mars228.0687 Jupiter778.64333 Saturn1427.410760 Uranus2838.230686 Neptune4497.860191 Pluto5913.590739

6 Planet Average Distance from the Sun (in millions of km) Time to Make Complete Orbit (in days) Mercury57.988 Venus108.2225 Earth149.6365 Mars228.0687 Jupiter778.64333 Saturn1427.410760 Uranus2838.230686 Neptune4497.860191 Pluto5913.590739

7 Planet Average Distance from the Sun (in millions of km) Time to Make Complete Orbit (in days) Mercury57.988 Venus108.2225 Earth149.6365 Mars228.0687 Jupiter778.64333 Saturn1427.410760 Uranus2838.230686 Neptune4497.860191 Pluto5913.590739

8 The function f(x) =. 199x 1.5 is called a power function A power function is a function of the form f(x) = cx k with c and x both positive. 1.If the exponent k is positive, then f is increasing. Larger values of k cause f to increase more rapidly. 2. If the exponent k is negative, then f decreases toward zero. Negative values of k that are larger in size cause f to decrease more rapidly. y =.199x 1.5 y =.199x 1.7 y =.199x –1.7

9 When a car skids to a stop on dry concrete pavement, the length L, in feet, of the skid marks is related to the speed, S, in miles per hour, of the car by the power function L =.039S 2 1.If a driver going 55 miles per hour on dry concrete jams on the brakes and skids to a stop, how long will the skid marks be? 2.A policeman investigating an accident finds skid marks 230 feet long. The speed limit in the area is 65 miles per hour. Is the driver of the car in danger of getting a speeding ticket? 3.If the length of the skid marks for a certain car are 80 feet long, how fast was the car traveling when it braked? 4.The same relationship holds for trucks over a certain weight, except the numerical coefficient is not.039. If a truck going 60 miles per hour leaves a skid mark 210 feet long, what is the new value of the coefficient to the nearest thousandth?

10 Researchers for the agriculture industry have determined that power functions can be used to model the relationship between the heights and weights of various animals. The power function that relates the height of a cow to its weight is given by the equation where H represents the height in inches, and w represents the weight in pounds. 1.Based on the model, what is the height of a cow whose weight is 500 pounds? (Answer to the nearest tenth of an inch.) 2.Based on the model, what is the weight of a cow whose height is 36.5 inches? (Answer to the nearest tenth of a pound.) Practice

11 Researchers for the agriculture industry have determined that power functions can be used to model the relationship between the heights and weights of various animals. The power function that relates the height of a horse to its weight is given by the equation H = cw.43 where H represents the height in inches, and w represents the weight in pounds.

12 Planet Average Distance from the Sun (in millions of km) Time to Make Complete Orbit (in days) Mercury57.988 Venus108.2225 Earth149.6365 Mars228.0687 Jupiter778.64333 Saturn1427.410760 Uranus2838.230686 Neptune4497.860191 Pluto5913.590739 How was this power function obtained?

13 Source: http://en.wikipedia.org/wiki/Charlotte,_North_Carolina YearPopulation 1940100,899 1950134,042 1960201,564 1970241,178 1980315,473 1990395,934 Charlotte, N.C. Population Plot the data points for population versus years since 1900 on your calculator. Charlotte, N.C. has seen rapid growth in the second half of the 20 th century. Now, it is the financial center of North Carolina, and its population is large enough to support a professional basketball team (the Bobcats) and football team (Panthers). The table shows the population of Charlotte in various years. 40 50 60 70 80 90

14 Source: http://en.wikipedia.org/wiki/Charlotte,_North_Carolina YearPopulation 1940100,899 1950134,042 1960201,564 1970241,178 1980315,473 1990395,934 Charlotte, N.C. Population Plot the data points for population versus years since 1900 on your calculator. Use power regression to find a power model for this data. Write the equation with coefficients rounded to three decimal places. Charlotte, N.C. has seen rapid growth in the second half of the 20 th century. Now, it is the financial center of North Carolina, and its population is large enough to support a professional basketball team (the Bobcats) and football team (Panthers). The table shows the population of Charlotte in various years. 40 50 60 70 80 90

15 Source: http://en.wikipedia.org/wiki/Charlotte,_North_Carolina YearPopulation 1940100,899 1950134,042 1960201,564 1970241,178 1980315,473 1990395,934 Charlotte, N.C. Population Plot the data points for population versus years since 1900 on your calculator. Use power regression to find a power model for this data. Write the equation with coefficients rounded to three decimal places. Charlotte, N.C. has seen rapid growth in the second half of the 20 th century. Now, it is the financial center of North Carolina, and its population is large enough to support a professional basketball team (the Bobcats) and football team (Panthers). The table shows the population of Charlotte in various years. 40 50 60 70 80 90

16 Source: http://en.wikipedia.org/wiki/Charlotte,_North_Carolina YearPopulation 1940100,899 1950134,042 1960201,564 1970241,178 1980315,473 1990395,934 Charlotte, N.C. Population Plot the data points for population versus years since 1900 on your calculator. Use power regression to find a power model for this data. Write the equation with coefficients rounded to three decimal places. Charlotte, N.C. has seen rapid growth in the second half of the 20 th century. Now, it is the financial center of North Carolina, and its population is large enough to support a professional basketball team (the Bobcats) and football team (Panthers). The table shows the population of Charlotte in various years. In what year does the model predict the population of Charlotte will pass one million?

17 Source: http://en.wikipedia.org/wiki/Charlotte,_North_Carolina YearPopulation 1940100,899 1950134,042 1960201,564 1970241,178 1980315,473 1990395,934 Charlotte, N.C. Population Plot the data points for population versus years since 1900 on your calculator. Use power regression to find a power model for this data. Write the equation with coefficients rounded to three decimal places. What is the model’s prediction for the population of Charlotte in the year 2010? Charlotte, N.C. has seen rapid growth in the second half of the 20 th century. Now, it is the financial center of North Carolina, and its population is large enough to support a professional basketball team (the Bobcats) and football team (Panthers). The table shows the population of Charlotte in various years. In what year does the model predict the population of Charlotte will pass one million?

18 Source: http://en.wikipedia.org/wiki/Charlotte,_North_Carolina YearPopulation 1940100,899 1950134,042 1960201,564 1970241,178 1980315,473 1990395,934 Charlotte, N.C. Population Plot the data points for population versus years since 1900 on your calculator. Use power regression to find a power model for this data. Write the equation with coefficients rounded to three decimal places. Charlotte, N.C. has seen rapid growth in the second half of the 20 th century. Now, it is the financial center of North Carolina, and its population is large enough to support a professional basketball team (the Bobcats) and football team (Panthers). The table shows the population of Charlotte in various years. What would have happened if we had used years since 1940? 1940 0 10 20 30 40 50

19 Source: http://en.wikipedia.org/wiki/Charlotte,_North_Carolina YearPopulation 1940100,899 1950134,042 1960201,564 1970241,178 1980315,473 1990395,934 Charlotte, N.C. Population Plot the data points for population versus years since 1940 on your calculator. Use power regression to find a power model for this data. Write the equation with coefficients rounded to three decimal places. Charlotte, N.C. has seen rapid growth in the second half of the 20 th century. Now, it is the financial center of North Carolina, and its population is large enough to support a professional basketball team (the Bobcats) and football team (Panthers). The table shows the population of Charlotte in various years. What would have happened if we had used years?

20 Source: http://en.wikipedia.org/wiki/Charlotte,_North_Carolina YearPopulation 1940100,899 1950134,042 1960201,564 1970241,178 1980315,473 1990395,934 Charlotte, N.C. Population Plot the data points for population versus years since 1900 on your calculator. Use power regression to find a power model for this data. Write the equation with coefficients rounded to three decimal places. Charlotte, N.C. has seen rapid growth in the second half of the 20 th century. Now, it is the financial center of North Carolina, and its population is large enough to support a professional basketball team (the Bobcats) and football team (Panthers). The table shows the population of Charlotte in various years. 40 50 60 70 80 90

21 Source: http://en.wikipedia.org/wiki/Charlotte,_North_Carolina YearPopulation 1940100,899 1950134,042 1960201,564 1970241,178 1980315,473 1990395,934 Charlotte, N.C. Population Plot the data points for population versus years since 1930 on your calculator. Use power regression to find a power model for this data. Write the equation with coefficients rounded to three decimal places. Charlotte, N.C. has seen rapid growth in the second half of the 20 th century. Now, it is the financial center of North Carolina, and its population is large enough to support a professional basketball team (the Bobcats) and football team (Panthers). The table shows the population of Charlotte in various years. 10 20 30 40 50 60 When using power model, you may have to experiment with different starting values in order to get the best possible fit.

22 Homework: Handout - Section 5.2

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