Final answer:
To find a linear function that models the data, we can use the slope-intercept form of a linear equation, which is y = mx + b. In this case, the linear function is S(x) = 19x - 36375.
Step-by-step explanation:
To find a linear function that models the data, we can use the slope-intercept form of a linear equation, which is y = mx + b, where y represents the sales in billions of dollars and x represents the year. We know that in 2011 online sales were 194 billion and in 2014 they were 251 billion. To find the slope, we can use the formula: slope = (change in y) / (change in x). This gives us a slope of (251 - 194) / (2014 - 2011) = 57 / 3 = 19. To find the y-intercept, we can substitute the coordinates of one of the points into the equation and solve for b. Let's use the point (2011, 194): 194 = 19 * 2011 + b. Solving for b, we get b = 194 - 19 * 2011 = -36375. Therefore, the linear function that models the data is S(x) = 19x - 36375.