A roast turkey is removed from an oven when its temperature has reached $185F$ and is placed on a table in a room where the ambient temperature is $75F.($Round your answers to the nearest whole number.$)$

$($a$)$ If the temperature of the turkey is $150F$ after half an hour, what is the temperature $($in $F)$ after $35$ minutes?

$T(35)=F$

$($b$)$ After how many minutes will the turkey have cooled to $95F?$

$t=$ min