For this exercise, you will create several recursive functions in order to get a better understanding of how recursion works.$$ In exercise $2,$ we will illustrate using recursion for creating art.$$

Create a new project in IntelliJ called Recursion.$$ Add a new Java class called Recursion with a public static main function.$$You will add several functions to your Recursion class as follows:

$1$ Write a recursive function int sum$($int n$)$ that adds up the numbers from n to $1$ and print your result.$$For example from main do the following:$$

Recursion recursion $=$ new Recursion$()$;

System.out.println$($recursion$.$sum$(6))$;

$1\mathrm{.}2$ Write a recursive function factorial$($int n$)$ that calculates the factorial of n$.$ Print out the results.$$ Add your function to your Recursion class.$$

$1\mathrm{.}3.$Write a recursive function powerOf$10($int n$)$ that calculates $10$n$.$

$1\mathrm{.}4.$ Write a more general recursive function powerOfN$($int x$,$ int p$)$ that calculates the power of xp$.$ Do not use the Math.pow function.$$

$1\mathrm{.}5.$ Write a function int bunnyEars$($int n$)$ that calculates the number of bunny ears for n bunnies.$$ Bunnies have two ears.$$