A fluid initially at $120$C is placed outside on a day when the temperature is $-30$C$,$ and the temperature of the fluid drops $20$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$)=$

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