Question

Ashley has 100 books that she wants to give away at the rate of n books per week. Write a recursive function that represents the number of books Ashley has at any time. The recursive function that gives the number of books Ashley has at any time is

Answer 1

X: represents how many weeks
N: represents books per week
B: represents books she has at anytime

So the recursive formula would be: 100 - XN = B

Answer 2

Answer:
`100-wn` , where w is the number of weeks (natural number) .

Explanation:

Given: Ashley has 100 books that she wants to give away at the rate of n books per week.

Let 'w' be the number of weeks .

Then after first week w=1,

The number of books Ashley has after first week =
`100-n`

[Since she wants to give away at the rate of n books per week.]

Then after second week w=2,

The number of books Ashley has after second week =
`100-n-n=100-2n`

Then after third week w=3,

The number of books Ashley has after third week =
`100-2n-n=100-3n`

Similarly for w weeks, the number of books Ashley has after w weeks =
`100-wn`

Hence, the recursive function that gives the number of books Ashley has at any time is
`100-wn`, where w is the number of weeks.