Question

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? The recursive function is , starting at .

Answer 1

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 = 20 2 = 21 4 = 22 8 = 23 16 = 24 . . . We start with 80 and we add 2n to it where n represents the number of days into the iteration with n starting at 0 The function that shows how many stamps we have on any given day is D S = 80 + ∑ 2n Where D is the number of days we are into the iteration n=0 NOTE: 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 have S = 80+20+21+22+23+24 = 80+1+2+4+ 8+16 = 111 stamps

Answer 2

Answer:

The reverse function is: next = now + 2^(n-1) starting at 80

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Step-by-step explanation: