Question

Suppose that the consumer price index​ (CPI), which measures the cost of a typical package of consumer​ goods, stood at 113.5 in 1990 and 133.5 in 2000. Let x equal 0 correspond to​ 1990, and estimate the CPI in 1992 and 2001. ​(Assume that the data can be modeled by a straight​ Which liner equation best models the cpI ?

a. y = 3x-110.2
b. y = -3x+ 110.2
c. y = 3x + 110.2

Answer 1

Answer:

Equation: y=2x+113.5

CPI in 1992 and 2001 are 117.5 and 135.5 respectively.

Step-by-step explanation:

Let x equal 0 correspond to​ 1990.

The cost of a typical package of consumer​ goods, stood at 113.5 in 1990 and 133.5 in 2000.

It is given that the data can be modeled by a straight. So, the line passes through (0,113.5) and (10,133.5).

The equation of line is

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-113.5=\dfrac{133.5-113.5}{10-0}(x-0)$

$y-113.5=2(x)$

$y=2x+113.5$            .... (1)

Therefore, the best liner equation that models the CPI is y=2x+113.5.

Note: The given options are incorrect.

We need to estimate the CPI in 1992 and 2001.

Substitute x=2 in equation (1), to find the CPI in 1992.

$y=2(2)+113.5=117.5$

Substitute x=11 in equation (1), to find the CPI in 2001.

$y=2(11)+113.5=135.5$

Therefore, the CPI in 1992 and 2001 are 117.5 and 135.5 respectively.