In $2004,$ the national debt was $$5,674$ billion. Then in $2022$ it reached $$30,824$ billion.

a$)$What$\text{'}$s the average annual growth rate from $2004$ to $2022?$

b$)$ If debt continues to grow at this rate, what will the national debt be in $2027$

c$)$ If the debt continues to grow at this rate $,$ when will it reach $$100,000$ billion?