Bob's car engine runs at $90C.$ On a day when the outside temperature is $20C,$ he turns off the ignition and notes that $5$ minutes later, the engine has cooled to $60C.$

$($a$)$ Determine the engine's cooling constant $k.$

$($b$)$ What is the formula for $y(t)?$

$($c$)$ When will the engine cool to $30C?$