Submit Test This Question: 8 pts 11 of 20 This Test: 130 pts possible E Question
ID: 3136691 • Letter: S
Question
Submit Test This Question: 8 pts 11 of 20 This Test: 130 pts possible E Question Help Suppose that the consumer price index (CPI), which measures the cost of a typical package of consumer correspond to 1990, and estimate the CPI in 1994 and 2002. (Assume that the data can be modeled by a straight line.) goods, stood at 130.9 in 1990 and 160.9 in 2000. Let x OA. OB, OC. y#3x-130.9 y=-3x + 130.9 y=3x+ 130.9 In 1994, the CPI would be approximately Type an integer or a decimal.) In 2002, the CPI would be approximately Type an integer or a decimal.)Explanation / Answer
(a).We know that if a line passes through the points (x1,y1) and (x2,y2), then its slope (m) is given by m = (y2-y1)/(x2-x1). Further, if its y-intercept is c, then its equation is y = mx+c. Here, in 1990, when x = 0, we have y = 130.9 and in 2000, when x = 10, we have y = 160.9. Then, the slope of the line representing changes in CPI is (160.9-130.9)/(10-0) = 30/10 = 3. Also, the CPI is 130.9 when x = 0 so that the y-intercept of the required line is 130.9.Thus, the linear function which best models the CPI is y = 3x+130.9. Option C is the correct answer.
(b). In 1994, when x = 4, we have CPI = y = 3*4 +130.9 = 12 +130.9 = 142.9. Thus, the CPI would be 142.9 (approximately) in 1994.
(c ). In 2002, when x = 12, we have CPI = y = 3*12 +130.9 = 36+130.9 = 166.9. Thus, the CPI would be 166.9 (approximately) in 2002.