Continuous/Categorical

In the section "Interacting a Categorical Variable with a Continuous Variable",

"For this model, the log(AoI) curve is in relation to the base class for sprinklers (i.e. No Sprinklers). The coefficient of the interaction term is estimated as -0.1032, so the AoI curve is less steep when sprinklers are present than otherwise. The mean claim frequency curve is proportional to AoI^0.3207 =AoI ^ 0.4239+−0.1032  when there is a sprinkler, and AoI^0.4239  when there is no sprinkler."


Why is not AoI^0.4239 * exp (-0.1032) ?

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