KNOW ALL BY THESE PRESENTS, that the undersigned hereby makes, constitutes
and appoints Dr. Reginald Brothers, Carolyn Blankenship and Sean Ricker, signing
singly, the undersigned's true and lawful attorneys-in-fact, with full power and
authority as hereinafter described on behalf of and in the name, place and stead
of the undersigned to:

     (i)     execute for and on behalf of the undersigned, in the undersigned's
             capacity as a director, director nominee, officer or beneficial
             owner of shares of common stock (the "Shares") of BigBear.ai
             Holdings, Inc., a Delaware corporation (the "Company"), any
             Schedule 13D or Schedule 13G, and any amendments, supplements or
             exhibits thereto (including any joint filing agreements) required
             to be filed by the undersigned under Section 13 of the Securities
             Exchange Act of 1934, as amended, and the rules and regulations
             promulgated thereunder (the "Exchange Act"), and any Forms 3, 4,
             and 5 and any amendments, supplements or exhibits thereto required
             to be filed by the undersigned under Section 16(a) of the Exchange

     (ii)    do and perform any and all acts for and on behalf of the
             undersigned which may be necessary or desirable to complete and
             execute any such Schedule 13D, Schedule 13G, Form 3, 4, or 5 and
             timely file such forms with the United States Securities and
             Exchange Commission and any stock exchange on which the Shares are
             then listed; and

     (iii)   take any other action of any type whatsoever in connection with the
             foregoing which, in the opinion of such attorneys-in-fact, may be
             of benefit to, in the best interest of, or legally required by, the
             undersigned, it being understood that the documents executed by
             such attorneys-in-fact on behalf of the undersigned pursuant to
             this Power of Attorney shall be in such form and shall contain such
             terms and conditions as such attorneys-in-fact may approve in such
             attorneys-in-fact's discretion.

     The undersigned hereby grants to such attorneys-in-fact full power and
authority to do and perform any and every act and thing whatsoever requisite,
necessary, or proper to be done in the exercise of any of the rights and powers
herein granted, as fully to all intents and purposes as the undersigned might or
could do if personally present, with full power of substitution or revocation,
hereby ratifying and confirming all that such attorneys-in-fact's substitute or
substitutes, shall lawfully do or cause to be done by virtue of this Power of
Attorney and the rights and powers herein granted. The undersigned acknowledges
that the foregoing attorneys-in-fact, in serving in such capacity at the
request of the undersigned, are not assuming, nor is the Company assuming, any
of the undersigned's responsibilities to comply with Section 13 and Section 16
of the Exchange Act.

     This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file reports or schedules under Section 13
or Section 16 of the Exchange Act with respect to the undersigned's holdings of
and transactions in securities issued by the Company, unless earlier revoked by
the undersigned in a signed writing delivered to the foregoing attorneys-in-

                                 *  *  *  *  *

     IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to be
executed as of this 13th day of June, 2022.

                                                  /s/ Julie Peffer

                                                  Name: Julie Peffer