In $1904,$ the first Putting Green Championship was held. The winner's prize money was $$150.$ In $2016,$ the winner's check was $$1,171,000.($Do not round intermediate calculations.$)$

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

b$.$ If the winner's prize increases at the same rate, what will it be in $2049?$