In $1895,$ the first U$.$S$.$ Putting Green Championship was held. The winner's prize money was $\backslash (\backslash$$ $210\backslash ).$ In $2022,$ the winner's check was $\backslash$$$3,550,000.$

a$.$ What was the percentage increase per year in the winner's check over this period?

Note: Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$

b$.$ If the winner's prize increases at the same rate, what will it be in $2057?$

Note: Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$

Answer is complete but not entirely correct.