Solve the problem. Give the value of $k$ in line $1.$ Give the model ascertained in line $2.$ Answer the question in line $3.$

Coffee is best enjoyed at a temperature of $116F.$ Discover the temp $T$ at which to should serve coffee so that it will have cooled to this ideal temperature in $6$ minutes. A cup of coffee served at $195F$ cools to $184F$ in one minute in a $71F$ room. If the room temp is kept at $71F,$ what initial temperature should coffee be served to meet the goal? Use Newton's law of cooling, $f(t)=T_0+C{e}^{-kt},$ where $f(t)$ is the temperature at time $t$ after being introduced into an environment with a constant temperature $T_0$ and $C$ and $k$ are constants.