A group of students wish to go bowling. There is a flat rate of $5 per student for shoe rental. It then costs $2.50 pergame up to 2 games total and then the cost is $2.00 per game after the first 2. If 6 students went, each rented shoes
and each rolled 3 games;
1. create a step function equation to calculate the cost per student per game
2. graph your step function
3. determine the total cost for this bowling outing

Answers

Answer 1

Answer:

Answer:

$c(g)=\left\{\begin{array}{lcl}(5)/(\lceil g\rceil)+2.5&\text{for}&0<g \le 2\n\n(6)/(\lceil g\rceil)+2&\text{for}&g>2\end{array}\right.$
see below
$72

Step-by-step explanation:

1. Since the function is supposed to give cost per game, it will be the stated cost per game (2.50 or 2.00) in addition to the quotient of the fixed cost and the number of games. For more than 2 games, the "fixed cost" is essentially the $5 shoe cost plus the premium on the first two games, an additional dollar.

For graphing purposes, we choose to use the "ceiling" function, so that any fractional game is charged at the price for the next higher integer number of games.

The "cost per game" function can be written as ...

$c(g)=\left\{\begin{array}{lcl}(5)/(\lceil g\rceil)+2.5&\text{for}&0<g \le 2\n\n(6)/(\lceil g\rceil)+2&\text{for}&g>2\end{array}\right.$

2. The graph is shown in the attachment.

3. The cost per game for 3 games is c(3) = 6/3+2 = 4, so the cost for 3 games for 1 student is 3·4 = 12. The cost for 6 students is then 6·12 = 72 dollars.

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