Question

At a bowling alley, the cost of shoe rental is $2.75 and the cost per game is $4.75. If f (n) represents the total cost of shoe rental and n games, what is the recursive equation for f (n)?

Answer 1

Since each game costs $4.75, we need to add this quantity to the expression every recursive call. Also, we have that f(0) = 2.75, which is the cost of shoe rental.

If we evaluate n = 1 and n = 2 on the following expression, we have:

`\begin{gathered} f(n)=f(n-1)+4.75 \\ f(1)=f(0)+4.75=2.75+2.75=7.5 \\ f(2)=4.75+f(1)=4.75+7.5 \end{gathered}`

notice that on f(2) we have the cost of one game plus the cost of the previous game and the shoe rental

therefore, the recursive equation for f(n) is f(n) = 4.75 + f(n-1)