Answer:

f(n)=0.9times f(n-1)+10, f(0) = 175, n > 0

Step-by-step explanation:

Given :

A store had 175 cell phones in the month of January.

Every month, 10% of the cell phones were sold and 10 new cell phones were stocked in the store.  

To Find:

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

Solution:

Let n be the number of months  

So, when n=0

f(0)=175

Now, after 1 month i.e. At n=1

Now we are given that Every month, 10% of the cell phones were sold and 10 new cell phones were stocked in the store.

The number of cell phone in store after 1 month =

175-10% of 175+10

Thus  f(1)=f(0)-10% of f(0)+10

f(1)=f(0)-0.1times f(0)+10

f(1) =f(0)(1-0.1)+10

f(1) =f(0)(0.9)+10

Similarly we can do till n months,Thus , we get

f(n)=0.9times f(n-1)+10, f(0) = 175, n > 0

Hence Option 4 is correct.