6. A hot piece of metal is dropped into a cool liquid. As the metal cools, its temperature \(T\) degrees Celsius, \(t\) minutes after it enters the liquid, is modelled by
$$T = 300 \mathrm { e } ^ { - 0.04 t } + 20 , \quad t \geqslant 0$$
- Find the temperature of the piece of metal as it enters the liquid.
- Find the value of \(t\) for which \(T = 180\), giving your answer to 3 significant figures. (Solutions based entirely on graphical or numerical methods are not acceptable.)
- Show, by differentiation, that the rate, in degrees Celsius per minute, at which the temperature of the metal is changing, is given by the expression
$$\frac { 20 - T } { 25 }$$
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