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The temperature \(T\) (in \(^\circ\)C) of a chemical reaction \(t\) minutes after it begins is modelled by the cubic function:$$ T(t) = -t^3 + 9t^2 + 22, \quad t \ge 0 $$
Find the initial temperature of the reaction.
Calculate the temperature after 4 minutes.
Determine how long it takes for the temperature to return to its initial value.
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