Question

Suppose that the consumer price index​ (CPI), which measures the cost of a typical package of consumer​ goods, stood at 139.7 in 1990 and 169.7 in 2000. Let x=0 correspond to​ 1990, and estimate the CPI in 1994 and 2004. ​(Assume that the data can be modeled by a straight​ line.)

Which linear equation best models the​ CPI?

A. y = 3 x + 139.7

B. y = -3 x + 139.7

C. y = 3 x -139.7

In 1994​, the CPI would be approximately _

​(Type an integer or a​ decimal.)

In 2004 the CPI would be approximately _.

​(Type an integer or a​ decimal.)

Answer 1

The linear equation model the CPI is y = 3x + 139.7 (option A)

In 1994, which is 4 years after 1990, hence x = 4

y = 3x+139.7
y = 3(4) + 139.7
y = 12 + 139.7
y = 151.7

In 1994, the CPI would be approximately 151.7

In 2004, which is 14 years after 1990, hence x = 14

y = 3x+139.7
y = 3(14) + 139.7
y = 42 + 139.7
y = 181.7

In 2004, the CPI would be approximately 181.7