Sally makes a deal with her mother. If Sally does all her chores today, she will get half a cookie. If she does her chores on the second day as well, she will get one cookie. If she does her chores on the third day, she will get two cookies. Each day in a row that she does her chores, Sally will get double the amount of cookies as the previous day. Let $C(n)$ give the number of cookies Sally gets on day $n$.

a) What is the growth factor?

b) What is the initial value?

c) Write a formula for $C(n)$.

d) How many cookies does Sally get on day 30?

Hint: