Problem 3. Consider the following recurrence, defined for n a power of 4 (for the time of some algorithm): T(n) = 3 if n = 1 2T(n/4) + 4n + 1 otherwise (a) Calculate T(16) by hand. Show your work. (b) Use the tree method to solve the recurrence exactly, assuming n is a power of 4. (c) Use the formula to calculate T(1). Show your work. (d) Use the formula to calculate T(4). Show your work. (e) Use the formula to calculate T(16). Show your work. (f) Use Mathematical Induction to prove that your formula is correct in general.

Write a program that uses a two-dimensional array to store the highest and lowest temperatures for each month of the year. the program should output the average high, average low, and the highest and lowest temper- atures for the year. your program must consist of the following functions: a. function getdata: this function reads and stores data in the two- dimensional array. b. function averagehigh: this function calculates and returns the average high temperature for the year. c. function averagelow: this function calculates and returns the aver- age low temperature for the year. d. function indexhightemp: this function returns the index of the highest high temperature in the array. e. function indexlowtemp: this function retur