Q:

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

Accepted Solution

A:
Answer:f(n) = f(n − 1) ⋅ 0.6 + 20, n > 0Step-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 + 20In equation form this can written as:Shipments in a week = 60% of shipments of previous week + 20For, nth week we can re-write this equation as:f(n) = 60% of f(n - 1) + 20orf(n) = f(n - 1) ⋅ 0.60 + 20For example for first week, replace n by 1 to find the number of shipments in week 1 and same goes for next weeks.