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You can only find orders based on experimental data so this depends on the reaction. If you double the concentration and nothing happens to the rate, this is a zero order reaction. If you double the concentration and the rate also doubles, this is a first order reaction. If you double the concentration and the rate is squared this is a second order reaction.
If you are talking about a first order reaction the doubling of a reactant means the reaction rate is doubled. If it's a second order reaction then the reaction rate is increase by a factor of x^2, where x would be your reaction rate.
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