Please answer these questions with detailed steps and reasoning

5. [Maximum mark: 14] As part of a long term research project, economists from the Department of Agriculture have been recording the price of a bale of wool and a bushel of wheat on a weekly basis. The economists started collecting the information on the 1st January 2021. After some time they realized that the the price for each item could be reasonably approximated by mathematical functions. The price, in dollars per bale of wool is given by WU) = 15 + 5605 (St5f) The price, in dollars per bushel of wheat is given by P (t) = 3: 60-05' + 5 , In each case, 1' is the number of weeks from the lst January 2021 (so that lst January corresponds to f = 0, 8th January corresponds to t = land so on). (a) Determine the price of wool and wheat on the following dates: i. 29 January 2021 . ii. 20th May 2021. iii. 2nd August 2021. (b) Give the amplitude and period of the function W. (0) Sketch the graphs of Wand P for (05 I 5 50). (d) What is the maximum price that the wheat reaches? (e) Estimate, from the graph, during which weeks, after the lst January 2021, the price of the wool and price of wheat are equal