Nathan has 80 stamps in his collection. he adds 1 stamp to it today. each day he plans to add twice the number of stamps as the previous day. if he keeps adding stamps at this rate for n days, which recursive function represents the number of stamps he has on any day in the future?

111
We start with 80 and we add 1 on the first day, 2 on the 2nd, 4 on the 3rd, etc.. Looking at the numbers being added 1   = 202   = 214   = 228   = 2316 = 24...We start with 80 and we add 2n to it where n represents the number of days into the iterationwith n starting at 0 The function that shows how many stamps we have on any given day is                 DS = 80 + ∑ 2n       Where D is the number of days we are into the iteration              n=0NOTE:  This starts at day 0 which would be S = 80 + 20 = 80 + 1 = 81 stamps Example:  To find how many stamps we have on D = 4  we would haveS =  80+20+21+22+23+24   =    80+1+2+4+ 8+16     = 111 stamps

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