6. As a substance cools its temperature, \(T ^ { \circ } \mathrm { C }\), is related to the time ( \(t\) minutes) for which it has been cooling. The relationship is given by the equation $$T = 20 + 60 \mathrm { e } ^ { - 0.1 t } , t \geq 0$$

1. Find the value of \(T\) when the substance started to cool.
2. Explain why the temperature of the substance is always above \(20 ^ { \circ } \mathrm { C }\).
3. Sketch the graph of \(T\) against \(t\).
4. Find the value, to 2 significant figures, of \(t\) at the instant \(T = 60\).
5. Find \(\frac { \mathrm { d } T } { \mathrm {~d} t }\).
6. Hence find the value of \(T\) at which the temperature is decreasing at a rate of \(1.8 ^ { \circ } \mathrm { C }\) per minute.