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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 .

with

Step-by-step explanation:

We can study what happens day by day starting with day one (1) to understand how the recursive relation can be constructed:

Day #     Number of stamps     What is added relative to previous day

1               d1 = 80 + 1 = 81

2              d2 = 81 + 2 = 83            d2 = d1 + 2

3              d3 = 83 + 4 = 87           d3 = d2 +

4              d4 = 87 + 8 = 95           d4 = d3 +

5              d5 = 95 + 16 = 111          d5 = d4 +

6              d6 = 111 + 32 = 143        d6 = d5 +

(n+1)                                               d(n+1) = dn +