A: Did you remember to take the rubbish out? B: Sorry, I didn't. I …. take it out in a minute. (am going to / will)

The correct choice is will. This is a spontaneous decision made at the moment of speaking. Be going to is used for pre-planned intentions, while will is for decisions made on the spot. The phrase "in a minute" indicates immediate future, and the speaker just decided, so will fits.

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