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30 April, 00:08

33 pts.

Is this a arithmetic or geometric sequence and answer the question. Show your steps

A store had 250 bottles of water. Each week, 40% of the bottles were sold and 48 new bottles arrived in shipments. Which recursive function best represents the number of bottles of water in the store, given that f (0) = 250?

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  1. 30 April, 01:08
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    It is neither a simple arithmetic nor geometric sequence, since it involves both a ratio and a difference.

    For week "n", 40% of the previous week's bottles were sold, so 60% is what's left, so what's left = f (n-1) * (1-40%) = 0.6f (n-1).

    48 bottles arrive, so we add 48 to what remains this week, giving

    f (n) = 0.6*f (n-1) + 48
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