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4.2.2 Solving Problems Given Functions Fitted to Data

4.2.2 Solving Problems Given Functions Fitted to Data. MCC9-12.S.ID.6a. Data with two quantitative variables can be represented using a______________. scatter plot. A ____________is a graph of data in two variables on a coordinate plane, where each data pair is represented by a point.

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4.2.2 Solving Problems Given Functions Fitted to Data

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  1. 4.2.2 Solving Problems Given Functions Fitted to Data MCC9-12.S.ID.6a

  2. Data with two quantitative variables can be represented using a______________. scatter plot A ____________is a graph of data in two variables on a coordinate plane, where each data pair is represented by a point. scatter plot Graphing a function on the same coordinate plane as a scatter plot for a data set allows us to see if the function is a good ____________of the relationship between the two variables in the data set. estimation

  3. Example 1 Andrew wants to estimate his gas mileage, or miles traveled per gallon of gas used. He records the number of gallons of gas he purchased and the total miles he traveled with that gas. Create a scatter plot showing the relationship between gallons of gas and miles driven. Which function is a better estimate for the function that relates gallons to miles: y = 10x or y = 22x? How is the equation of the function related to his gas mileage?

  4. ✔ 640 600 560 520 480 440 400 360 320 280 240 y=22x 200 Plot the points. 160 120 y=10x Graph y=10x 80 40 Graph y=22x 2 4 6 8 10 12 14 16 18 20

  5. The graph of the function ________goes through approximately the center of the points in the scatter plot. The function ________ is not steep enough to match the data values. The function ________ is a better estimate of the data. y = 22x y = 10x y = 22x For the equation that models the data the slope represents: or 22 miles per gallon.

  6. Example 2 The principal at Park High School records the total number of students each year. The table to the right shows the number of students for each of the last 8 years. Create a scatter plot showing the relationship between the year and the total number of students. Show that the function y = 600(1.05)x is a good estimate for the relationship between the year and the population. Approximately how many students will attend the high school in year 9?

  7. 1000 950 900 850 800 750 700 1. Plot the points. 650 600 550 500 450 400 350 300 250 200 150 100 50 2 4 6 8 10 12 14 16 18 20

  8. 1000 ✔ 950 900 Graph y = 600(1.05)x on the coordinate plane. 850 800 750 700 650 600 550 500 450 400 350 300 250 200 150 100 50 2 4 6 8 10 12 14 16 18 20

  9. The function y = 600(1.05)x is a good estimate of the population. 3. Use the function to estimate the population in year 9. • Evaluate the function y = 600(1.05)x for year 9, when x = 9. • y = 600(1.05)9 = 930.797 • There will be approximately 931 students in the school in year 9.

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