A store had 235 MP3 players in the month of January. Every month, 30% of the MP3 players were sold and 50 new MP3 players were stocked in the store.

Which recursive function best represents the number of MP3 players in the store f(n) after n months?

A. f(n) = 0.7 × f(n - 1) + 50, f(0) = 235, n 0
B.f(n) = 237 - 0.7 × f(n - 1) + 50, f(0) = 235, n 0
C.f(n) = 0.3 × f(n - 1) + 50, f(0) = 235, n 0
D.f(n) = 237 + 0.7 × f(n - 1) + 50, f(0) = 235, n 0

Question

A store had 235 MP3 players in the month of January. Every month, 30% of the MP3 players were sold and 50 new MP3 players were stocked in the store.

Which recursive function best represents the number of MP3 players in the store f(n) after n months?

A. f(n) = 0.7 × f(n - 1) + 50, f(0) = 235, n > 0
 B.f(n) = 237 - 0.7 × f(n - 1) + 50, f(0) = 235, n > 0
 C.f(n) = 0.3 × f(n - 1) + 50, f(0) = 235, n > 0
 D.f(n) = 237 + 0.7 × f(n - 1) + 50, f(0) = 235, n > 0

afrodiddle · Answer

I believe  it is A) but I am not entirely sure, can someone walk me through the steps?

anonymous · Answer

i agree, it is A.
the first term $$0.7\times f(n-1)$$ represents 70% of the total MP3 players of the previous month, that is the remaining quantity since 30% were sold.
the other term +50, represents the newly added MP3 players to the stock
and if January is indexed by n=0, f(0) should be 235, as is in answer A
so, answer A matches all the requirements!