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Name Date Pd Scientific Methods Worksheet 3: Graphical Analysis 1. A friend prepares to place an online order for CD's. a. What are the units for the slope of this graph? Slope = 7 y-intercept = 3.6 dollars compact disc b. What does the slope of the graph tell you in this situation? The average cost of one compact disc in dollars. c. Write an equation that describes the graph. $ C (7.0 CD )M d. Provide an interpretation for what the y-intercept could mean in this situation. The shipping cost for the order. 2. The following times were measured for spheres of different masses to be pushed a distance of 1.5 meters by a stream: Time (s) 20 30 Time (s) 10.2 17.3 23.8 31.0 0 a. Graph the data by hand on the grid provided and write a mathematical model for the graph that describes the data. 10 Mass (kg) 5 10 15 20 t (1.4 kgs )m 3.5s 0 5 10 Mass (kg) 15 b. Write a clear sentence that describes the relationship between mass and time. The change in time is directly proportional to the change in mass. ©Modeling Instruction - AMTA 2013 1 U1 Scientific Methods ws3 v3.1 20 3. A student performed an experiment with a metal sphere. The student shot the sphere from a slingshot and measured its maximum height. The sphere was shot six times at six different angles above the horizon. a. What is the relationship being studied? The relationship between the maximum height of the sphere and the angle at which the sphere was shot. b. What is the independent variable in this experiment? The angle at which the sphere was shot. c. What is the dependent variable in this experiment? The maximum height of the sphere. d. What variables must be held constant throughout this experiment? The slingshot must be stretched the same amount each trial. The sphere must leave the slingshot at the same height during each trial. 4. a. What type of relationship does this graph suggest? The square of the accidents are proportional to the age. b. What variables would you plot to linearize the data? The square of the number of accidents vs. the age. ©Modeling Instruction - AMTA 2013 2 U1 Scientific Methods ws3 v3.1 5. Consider the graph at right. a. Write a mathematical expression that describes the relationship. The scholarships are directly proportional to the effort. b. Provide an interpretation for the intercept. y- If there is no effort, there will be no scholarships. c. Using the equation, predict how many applications would be needed to earn $8000. $ s (500 app )e e $8,000 16app $ 500 app 6. For each of the following graphs: a. Describe how you would linearize the graph. Assuming a linear test plot results, write the equation that would describe the straight line produced. Take the inverse of the x values and test plot y vs. 1 m y m( ) y x x y 1 x x b. y Square the x values and test plot y vs. x2. y mx 2 x Square the y values and test plot y2 vs. x. y 2 mx c. y x ©Modeling Instruction - AMTA 2013 3 U1 Scientific Methods ws3 v3.1 7. The graph below compares the amount of time it takes a planet to orbit the sun (in earth days) versus the distance the planet is from the sun, measured in Astronomical Units. (1 AU = earth to sun separation.) a. What test plot would you try first in order to linearize the relationship below? Square the x values and test plot y vs. x2. b. In this case it turns out that several test plots need to be made before the graph is linearized. (Johannes Kepler was the first person to work out this relationship in the early 1600's.) Write the equation for the graph below. Does the same equation apply to the graph above? Why? 3 yr Both graphs have the same equation. Both graphs represent the same relationship 2 1.00 AU 3 r 2 in a different fashion. The first graph plots y vs. x and the 2nd y2 vs. x3. ©Modeling Instruction - AMTA 2013 4 U1 Scientific Methods ws3 v3.1