The changes in prices of a cubic metre of oak wood and a cubic metre of pine wood between 2013 and 2020 are presented in table 1. The prices of a cubic metre of oak wood and a cubic metre of pine wood in 2014 and 2020 are presented in table 2. TABLE 1: Chain index numbers for the prices of a cubic metre of oak wood and a cubic metre of pine wood (2014-2020) 2015 2016 Year Oak wood Pine wood 2014 1.01 1.02 0.89 1.11 2017 1.16 1.06 2018 1.22 0.97 2019 1.04 0.95 2020 1.26 1.09 1.1 TABLE 2: Prices of a cubic metre of oak wood and a cubic metre of pine wood in 2014 and in 2020 Price Oak wood Pine wood 2014 300 200 2020 510 y a) Find x and y b) By how much (percentagewise) did the price of a cubic metre of pine wood change between 2016 and 2020? c) Find the average rate of change for the price of pine wood between 2015 and 2020. Assuming that the same average rate of change will apply to subsequent years, approximate the price of a cubic metre of pine wood in 2022. d) In one of the counties in western Poland consumers bought 500 cubic metres of pine wood and 100 cubic metres of oak wood in 2014. In 2020 they bought 400 cubic metres of pine wood and 200 cubic metres of oak wood. Find the Paasche price index given the prices and quantities as above. The changes in prices of a cubic metre of oak wood and a cubic metre of pine wood between 2013 and 2020 are presented in table 1. The prices of a cubic metre of oak wood and a cubic metre of pine wood in 2014 and 2020 are presented in table 2. TABLE 1: Chain index numbers for the prices of a cubic metre of oak wood and a cubic metre of pine wood (2014-2020) 2015 2016 Year Oak wood Pine wood 2014 1.01 1.02 0.89 1.11 2017 1.16 1.06 2018 1.22 0.97 2019 1.04 0.95 2020 1.26 1.09 1.1 TABLE 2: Prices of a cubic metre of oak wood and a cubic metre of pine wood in 2014 and in 2020 Price Oak wood Pine wood 2014 300 200 2020 510 y a) Find x and y b) By how much (percentagewise) did the price of a cubic metre of pine wood change between 2016 and 2020? c) Find the average rate of change for the price of pine wood between 2015 and 2020. Assuming that the same average rate of change will apply to subsequent years, approximate the price of a cubic metre of pine wood in 2022. d) In one of the counties in western Poland consumers bought 500 cubic metres of pine wood and 100 cubic metres of oak wood in 2014. In 2020 they bought 400 cubic metres of pine wood and 200 cubic metres of oak wood. Find the Paasche price index given the prices and quantities as above