Question

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?

A: f(n) = f(n − 1) ⋅ 0.6 + 48, n > 0
B: f(n) = 250 − f(n − 1) ⋅ 0.4 + 48, n > 0
C: f(n) = f(n − 1) ⋅ 0.4 + 48, n > 0
D:f(n) = 250 − f(n − 1) ⋅ 0.6 + 48, n > 0

Answer 1

Option: A is the correct answer.

A: f(n) = f(n − 1) ⋅ 0.6 + 48, n > 0

Explanation:

It is given that:

A store had 250 bottles of water.

Each week, 40% of the bottles were sold and 48 new bottles arrived in shipments.

This means that the number of bottles that will be present in the store after 40% of the bottles will be sold at a particular week= 100%-40%=60% plus 48 new arrival

This means that each time the number of bottles in the store will be 60% of the bottles that were sold previous week plus 48.

Hence, if f(n-1) represent the number of bottle in the (n-1)th week then the number of bottles in the nth week will be represented by:

`f(n)=60\%\ of\ f(n-1)+48\\\\i.e.\\\\f(n)=0.6\cdot f(n-1)+48`

Answer 2

Let f(n) represent the number of bottles in the store on n-th week.

When n=0, f(n)=250.

Then 40% of the bottles were sold, this means that were sold 250·0.4=f(n)·0.4. The amount of bottles left is 250-250·0.4=f(n)-f(n)·0.4=f(n)·0.6.

If 48 new bottles arrived in shipments, then the amount of bottles became

f(n)·0.6+48=f(n+1).

Since n>0, then

f(n)=f(n-1)·0.6+48.

Answer: correct choice is A.