What is the answer?

Question

In 2001 there were 6680 electric-powered vehicles in use in the United States. In 1998 only 4760 electric vehicles were being used. 

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. Used ordered pair of the form (years past 1998, number of vehicles) B. Use this equation to predict the number of electric-powered vehicles in use in 2012.

Answer 1

Let x = years since the start in 1998 of data , so x= (t-1998), where

      t = year number (e.g, 2005)

Let y = number of electric powered vehicles

 

The general straight line is written as y = mx + b

So   y = m(t-1998) + b

In year t = 1998 , y = 4760,  so 4760 = m (0) + b,  hence the y-intercept is b = 4760

In year t = 2001 , (t-1998) = 3 and y = 6680 = m(3) + 4760,  so 3m = 6680 - 4760 = 1920, and m = 640

 

Hence, the linear relationship becomes the line:  y = 640(t-1998) + 4760   for all t >= 1998

 

And in 2012, (t-1998) = (2012 - 1998) = 14

y = 640(14) + 4760 = 8960 + 4760     =  13,720 electric cars.