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?

Question

Mathematics

Remington Wolf

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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Answers (1)

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Esperanza Terrell · Answer 1

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