The average price per square foot for office space in Denver, CO was $$25\mathrm{.}50$ in $2005,$ and it

was $$56\mathrm{.}60$ in $2016.$

a$)$ Find a model for which these data in which t $=0$ corresponds to $2005.$

b$)$ If this model were to remain accurate, what was the rent per square foot in $2018$