Question

The Consumer Price Index (CPI), which measures the cost of a typical package of consumer goods, was 202.2 in 2011 and 244.6 in 2016. Let x = 11 correspond to the year 2011 and estimate the CPI in 2014 and 2015. Assume

that the data can be modeled by a straight line and that the trend continue indefinitely Use two data points to find such a line and then estimate the requested quantities

Answer 1

• y = 8.48x + 108.92
• 227.64
• 236.12

Explanation:

According to given we have (x, y) pairs:

• (11, 202.2) and (16, 244.6)

Work out the equation of the line.

Find the slope:

• m = (244.6 - 202.2)/(16 - 11) = 8.48

Find the y- intercept using one pair of coordinates:

• 202.2 = 8.48*11 + b
• b = 202.2 - 93.28
• b = 108.92

The line is:

• y = 8.48x + 108.92

Find the value of y when x = 14 and x = 15:

• y = 8.48*14 + 108.92 = 227.64
• y = 8.48*15 + 108.92 = 236.12