Question

At a bowling alley, the cost of shoe rental is $2.55 and the cost per game is $3.75. If f (n) represents the total cost of shoe rental and n games, what is the recursive equation for f (n)?

f (n) = (2.55 + 3.75)n, n > 0
f (n) = 2.55 + 3.75n, n > 0
f (n) = 2.55 + 3.75 + f (n − 1), f (0) = 2.55
f (n) = 3.75 + f (n − 1), f (0) = 2.55

Answer 1

Recall that in a recursive definition you start by defining the first term f(0) and each subsequent f(n) term is defined in terms of the previous term f(n-1)z

The $2.55 shoe rental is a one-time cost at the very beginning even at 0 games, so f(0) would start at 2.55. From there, each game costs $3.75 so each subsequent value would add on an additional 3.75.

With that in mind, which formula do you think best represents this sequence?

Answer 2

Like I mentioned, a recursive definition must include defining f(0). Additionally, the function is defined in terms of f(n-1) not simply n. Therefore this automatically eliminates the first two options.

Answer 3

Good