In 2001 there were 6680 electric-powered vehicles in use in the United States. I

Question

In 2001 there were 6680 electric-powered vehicles in use in the United States. In 1998 only 4760 electric vehicles were being used. (Source: U.S. Energy Information Administration) a. Assume that the relationship between time, x, and number of electric-powered vehicles, y, is linear. Write an equation in slope-intercept form describing this relationship. Use ordered pairs of the form (years past 1998, number of vehicles). The equation is Type your answer in slope-intercept form.) b. Use this equation to predict the number of electric-powered vehicles in use in 2005 ehicles

Explanation / Answer

a. We know that the slope (m) of a line passing through the points (x1,y1) and (x2,y2) is given by m = (y2-y1)/(x2-x1).

Here, m = (6680-4760)/((2001-1998) = 1920/3 = 640.

Let the required linear function be y = mx +c, where m is the slope of the line, c is the y-intercept ( y-value when x = 0). Let us also assume that x represents the number of years past 1998 and y represents the number of electric powered vehicles. In 1998, when x = 0, we have y = 4760. Hence c = 4760. Thus, the required linear function is y = 640x + 4760.

b.In 2005, x = 7 so that y = 640*7 +4760 = 4480+4760 = 9240. Thus, in 2005, there will be 9240 electric powered vehicles.

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