Kayla’s Workout
Fast food has become a part of the busy American lifestyle. Experts point out that fast food is often high in calories.
Kayla eats fast food often. To maintain her weight, Kayla exercises on her bicycle. She knows one hour of bicycling burns many calories. Kayla also knows a female should eat about 2,000 calories per day to maintain her weight.
1. What does the point (10, 3500) on the graph mean? ______
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2. Write a function or specific rule to show the relationship between the number of hours on a bicycle and the number of calories burned. Be sure to define your variables. ______
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Show your work using words, numbers and/or diagrams.
A function or specific rule is a formula expressing a relation between two things. E.g. y = 2x the rule is y-values are twice the amount of the x-value
a. What is the slope of the line? ______
{The slope is the quotient of the change in vertical units to the change in horizontal units.}
b. What is the y-intercept of the line? ______
{The y-intercept is the point (ordered pair) where a graph crosses the y-axis.}
c. What does the slope mean in the context of this problem? ______
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d. What does the y-intercept mean in the context of the problem? ______
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e. Which variable is dependent (responding)? ______
The dependent variable is “ruled” by the independent variable. The height of a person depends, is ruled by: age, growth hormones, genetics, and other factors such as nutrition. In y = 2x the y-value will depend, is ruled by what x-value is used; y is the dependent variable.
f. Which variable is independent (manipulated)? ______
The independent variable is the variable we can often choose (manipulate); we can allow the independent variable to be a number and then calculate the dependent variable.
In y = 5x if we let x = 1, 2, and 3, then the y-values are: 5•1 =5, 5•2 =10, and 5•3 =15; the x-values were chosen and we calculated the y-values. The x-values were independent and the y-values dependent or restricted to 5, 10, and 15 because of our rule y = 5x and on the x’s we choose.
3. Kayla will go bicycling three days a week for one hour a day. Predict how many calories she will
burn in a week. ______
Show your work using words, numbers, and/or diagrams.
4. How long does Kayla have to ride her bicycle to burn up calories from a hamburger, fries, and a
soda if the meal has a total of 1,155 calories? ______
Show your work using words, numbers, and/or diagrams.
5. Kayla tends to eat an average of 2,100 calories per day. How many hours per week does she need
to bicycle to maintain her weight? ______
Show your work using words, numbers, and/or diagrams.
ELEANOR’S WORKOUT
6. Eleanor uses 10 calories of energy in warming up for her morning run. In addition, for every minute of running time, she uses 15 calories. She wants to know how many minutes she will need to run to burn up 1,000 calories.
a. Write an equation that would allow her to determine how many minutes she will need to
run to burn up 1,000 calories. ______
Show your work using words, numbers and/or diagrams.
b. What do the variables represent? ______
______
c. What is the slope of the line? ______
d. What is the y-intercept of the line? ______
e. What does the slope mean in the context of this problem? ______
______
f. What does the y-intercept mean in the context of the problem? ______
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g. Graph the equation for Eleanor’s workout so that another person would be able to access the same information from the graph as the equation. Remember to title the graph, label each axis, and use appropriate scales.
LEG BONE PROBLEM
Anthropologists and archaeologists often try to determine the height of a person from the size of the bones they find. Anthropologists know the height of a person and the length of their upper leg bone, the femur, are related.
This table was created last year call it data set A:
length of femur in inches / 14 / 16 / 21 / 15 / 11height of person in inches / 54 / 62 / 71 / 59 / 46
Each student measures his/her own femur and enters that value in the chart. Ask six (6) more students in the class for their femur measurement and height.
Put the data collected by you and six other students in the table; this table is data set B:
length of femur in inchesheight of person in inches
7. Graph both sets of data with the height as a function of femur length.
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8. Define the dependent (responding) variable? ______
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9. Define the independent (manipulated) variable? ______
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10. Draw a line that best fits last year’s data (data set A).
a. Choose two points on that line. ______
b. Determine the slope between these two points. ______
Show your work using words, number and/or diagrams.
c. Determine y-intercept of the line. ______
d. Write an equation of the line for last year’s data. ______
Show your work using words, number and/or diagrams.
11. Using a different color, draw a line that best fits the data for your class (data set B).
a. Choose two points on this line. ______
b. Determine the slope between these two points. ______
Show your work using words, number and/or diagrams.
c. Determine the y-intercept of the line. ______
d. Write an equation of the line for your class data. ______
Show your work using words, number and/or diagrams.
12. Give the values and meanings of the slopes of your lines within the context of this situation.
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13. Give the values and meanings of the y-intercepts of your lines within the context of this situation.
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14. Use your equations of the fitted lines to predict:
a. The height of a person whose femur was 18.25 inches long.
Height (data set A) ______Height (data set B) ______
Show your work using words, numbers, and/or diagrams.
b. The femur length of a person who was 71 inches tall.
Length (data set A) ______Length (data set B) ______
Show your work using words, numbers, and/or diagrams.
The Robert Wadlow Story
Born: February 22, 1918 Died: July 15, 1940
Robert Pershing Wadlow was born, educated and buried in Alton, Illinois. His height of 8’ 11.1” qualifies him as the tallest person in history, as recorded in the Guinness Book of Records. At the time of his death he weighed 490 pounds. At birth he weighed a very normal eight pounds, six ounces. He drew attention to himself when at six months old he weighed 30 pounds. A year later, at 18 months, he weighed 67 pounds. He continued to grow at an astounding rate, reaching six feet, two inches and 180 pounds by the time he was nine years old.
GROWTH CHART FOR ROBERT WADLOW
Age (yrs)
/ 5 / 8 / 10 / 14 / 16 / 20 / 21 / 22.4Height
(in) / 64 / 72 / 77 / 89 / 94 / 103 / 104 / 107.1Weight
(lbs) / 105 / 169 / 210 / 301 / 374 / 488 / 492 / 49015. Graph the data on two separate graphs; height on one graph and weight on the other graph.
(Do this on the next page)
16. Determine the dependent (responding) and independent (manipulated) variable. Explain your thinking for the choices you made?
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17. Draw a line that best fits the data for each graph and write the equation for each line.
Height equation: ______
Weight equation: ______
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18. Use your model, best fit line, to estimate how tall Robert was at age 14? ______
19. Use your model, best fit line, to determine how tall Robert would have been if he had lived to be 35 years old. ______
20. For the graph of Roberts’s height, what is the y-intercept of the graph? ______
a. What does this y-intercept represent in this situation? Does the y-intercept have meaning? Explain.
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b. What is the slope of the height line? ______
c. What meaning does the slope have in this situation?
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21. Using your model, how much does Robert weigh at: 17 years old? _____, 35 years old? ______
a. What is the y-intercept of the line? ______
b. What is the slope of the weight line? ______
c. Does the y-intercept match what was stated in the first paragraph about Robert? Why or why not?
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d. What meaning does the slope have in this situation?
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22. Is a linear function appropriate to use when graphing a person’s growth? Explain/support your answer.
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FASTFOOD WORKOUT MULTIPLE CHOICE PRATICE
23. The bar graph describes the speed of four runners in a recent race.
Which conclusion is true?
A. Everyone ran faster than 6 meters per second.
B. The best possible rate for the 100-meter dash is 5 meters per second.
C. The first-place runner was four times as fast as the fourth-place runner.
D. The second-place and third-place runners were closest in time to one another.
24. The left side of a solid block is held at a constant temperature of 200°C. The temperature within the block is given by where x is the distance, in centimeters, from the left side of the block and T is the temperature in degrees Celsius at location x.
What is the distance, x, when the temperature, T, is 50°C?
A. x = 5 cm
B. x = 10 cm
C. x = 15 cm
D. x = 20 cm
25. The number of games won over four years for three teams is shown on the graph below.
Which statement is true based on this information?
A. Team 3 always came in second.
B. Team 1 had the best average overall.
C. Team 1 always won more games than Team 3.
D. Team 2 won more games each year than in the previous year.
26. The bar graph represents the numbers of blocks each of 10 students walks to school each day.
Which is the median number of blocks that these students walk to school each day?
A. 3.5
B. 4.0
C. 4.5
D. 5.0
Student: Ch. 25 “Fast Food Workout 2” 5/02/08 Page 1 of 15