Problem $5-13$ Calculating Interest Rates and Future Values $[$LO$1,3]11\mathrm{.}11$pointseBookHintPrintReferencesIn $1895,$ the first U$.$S$.$ Putting Green Championship was held. The winner's prize money was $$170.$ In $2022,$ the winner's check was $$3,000,000.$a$.$ 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 $2051?$Note: Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$a$.$ Increase per yearb. Winners prize in $2051$