A fluid initially at $140$C is placed outside on a day when the temperature is $-30$C$,$ and the temperature of the fluid drops $40$C in one minute. Let T$($t$)$ denote the temperature, in Celsius, at time t$,$ in minutes.

$($a$)$ Find the temperature T$($t$)$ of the fluid for t$>0.$

T$($t$)=$

$($b$)$ Compute the limit$.$

limt$$T$($t$)=$