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Published byLaurence Farmer Modified over 9 years ago
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Chapter 2 Using lines to model data Finding equation of linear models Function notation/Making predictions Slope as rate of change
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2.1 Using lines to model data Records were taken over a period of 5 years of the numbers of baby girls born in Linea Hospital. The data is shown in the chart below. YearBaby Girls 2005413 2006482 2007502 2008565 2009641
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Scattergram A graph of plotted ordered pairs Should include: –scaling on both axes –labels of variables and scale units Number of girls born
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Approximately Linearly Related Sketch a line that comes close to (or on) the data points There are multiple lines that will reasonably represent the data.
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Definitions Approximately linearly related – a set of points in a scattergram of data that lie close to/or on a line Model – mathematical description of an authentic situation Linear model – linear function, or its graph, that describes the relationship between two quantities in an authentic situation.
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Making Predictions with Linear Models Approximately how many babies will be born in 2010? –708 When were 500 babies born? –Sept 2006
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When to Use a Linear Function to Represent Data
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Scattergrams are used to determine if variables are approximately linearly related. Warning: Draw the line that comes close to all data points, not the greatest number of points
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Intercepts of a model Let t be the years after 1950, let p be the polar bear population. Sketch a linear function to describe the relationship What does the p-intercept represent? –Population of 24,000 polar bears in 1970 When will the polar bears become extinct? –2015 Years Since 1970 10203040 4 12 20 p t
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For a function with independent variable t : –interpolation : when part of the model used whose t-coordinates are between the t- coordinates of two data points –extrapolation: when part of the model used whose t-coordinates are not between the t- coordinates of any two data points more faith losing faith no faith model breakdown – when prediction doesn’t make sense or estimate is a bad approximation
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Modifying a model In 2005, there were 6, recorded polar bears Modify to show the population leveling out at 8,000 polar bears. Modify to show polar bears becoming extinct.
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Group Exploration p 62-63
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Quiz Vocabulary Identify independent/dependent variable Find the equation of a line given a graph or graph the line give the equation Change an equation to slope intercept form Determine if lines are parallel, perpendicular or neither.
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