2. A whisky distiller named Taketsuru Masataka puts 8000L of whisky into barrels for aging, with 200L of whisky per barrel. Each year the volume of whisky in each barrel reduces by 2% due to evaporation (this is known as the angels' share). For the first 11 years after barreling, Taketsuru sells 2 barrels for 20 dollars per litre at the end of each year. Write bn for for the volume of whisky in each barrel at the beginning of year n, write Un for the total volume of whisky in storage at the beginning of year n, and rn for the total revenue from selling whisky at the beginning of year n. (a) Find a direct formula for bn. (b) Calculate the values of v₁, V2, V3 and then find a recursive definition for Un. (c) Find a recursive definition for rn. (d) Write a MATLAB program to compute Un and rn for n = = 1, 2 . . . 12 and display the values in three columns n, rn, Un with appropriate headings. (e) At the end of the 12th year Taketsuru finds that he can sell 12-year old whisky at the higher price of 50 dollars per litre. If he sells half of the remaining whisky at this price, how much money does he get?