PVT PLT OF AN SMA SEL CLBED INTO CLASS B AIRSPACE AFTER DEPARTING FROM AN UNDERLYING ARPT OF THE TCA.

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I MARKED 'PAX FLT' ABOVE; NOT BECAUSE I HAD PAYING PAX; BUT I WAS DOING A FAVOR FOR MY FRIEND BY PICKING UP HIS MOM SO SHE COULD SEE HIS COLLEGE GRADUATION. WE WERE ON A TIGHT SCHEDULE; SO ONCE I LANDED AT YIP (HAVING COME FROM AID) I DID EVERYTHING AS EXPEDIENTLY AS POSSIBLE. THIS CAUSED ME TO LEAVE MY SECTIONAL IN THE BACK SEAT. I REALIZED THIS ON TKOF; BUT IT DIDN'T BOTHER ME SINCE I HAD JUST COME INTO THE AREA USING IT; AND I HAD SET MY LORAN FOR NAV BEFORE TKOF. I MADE THE MISTAKE OF MAKING MY CHIEF CONCERN MY PAX; WHO HAD NEVER BEEN IN A LIGHT ACFT PREVIOUSLY. IT WAS VERY CHOPPY (TURB) AFTER TKOF; AND I KNEW FROM HAVING JUST COME IN THAT IT WAS THAT WAY BELOW 7500 FT MSL. FEARFUL OF MY PAX GETTING AIRSICK; I FOOLISHLY FOCUSED MOST OF MY ATTN ON GETTING ABOVE 7500 FT MSL AS QUICKLY AS POSSIBLE. BECAUSE MY SECTIONAL WAS NOT IN MY LAP (AS IT USUALLY IS); I DIDN'T HAVE A REMINDER THAT I WAS DIRECTLY BELOW DETROIT'S TCA; WHICH BEGAN AT 3300 FT MSL WHERE I WAS. I UNKNOWINGLY CLBED UP INTO THE TCA; WHEN AT 3500 FT MSL; THE YIP CTLR WHO HAD NOT YET CLRED ME OF THE AREA (FREQ CHANGE APPROVED); REMINDED ME OF MY ALT (BEING RPTED BY MODE C) AND THE ALT AND WHICH THE TCA BEGAN. HE 'SUGGESTED' I DSND TO UNDER 3300 FT MSL; AS THIS COULD BE A POSSIBLE AIRSPACE VIOLATION. I'M THANKFUL FOR THE CTLR'S REMINDER; OR I PROBABLY WOULD HAVE CONTINUED CLBING HIGHER INTO THE TCA. I IMMEDIATELY DSNDED TO 3100 FT MSL; WHERE I STAYED UNTIL CLR OF THE AREA. I WAS NEGLIGENT IN THAT I ALLOWED THE POSSIBILITY OF MY PAX GETTING MOTION SICKNESS TO OVERRIDE MY ORIENTATION WITH MY IMMEDIATE SURROUNDINGS; WHICH TURNED OUT TO BE DIRECTLY UNDER A TCA.