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14 July, 19:55

A store had 50 bottles of olive oil. Each week, 40% of the olive oil bottles were sold and 20 new bottles arrived in shipments. Which recursive function best represents the number of bottles in the store, given that f (0) = 50?

f (n) = f (n - 1) ⋅ 0.6 + 20, n > 0

f (n) = 50 - f (n - 1) ⋅ 0.6 + 20, n > 0

f (n) = 50 - f (n - 1) ⋅ 0.4 + 20, n > 0

f (n) = f (n - 1) ⋅ 0.4 + 20, n > 0

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  1. 14 July, 21:13
    0
    f (n) = f (n - 1) ⋅ 0.6 + 20, n > 0

    Step-by-step explanation:

    Each week 40% of the olive oil bottles were sold. This means, each week 60% of the bottles were left. In addition to these, 20 new bottles arrived in shipments.

    So, every week the number of shipments was:

    60% of the shipments of previous week + 20

    In equation form this can written as:

    Shipments in a week = 60% of shipments of previous week + 20

    For, nth week we can re-write this equation as:

    f (n) = 60% of f (n - 1) + 20

    or

    f (n) = f (n - 1) ⋅ 0.60 + 20

    For example for first week, replace n by 1 to find the number of shipments in week 1 and same goes for next weeks.
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