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Your total cost C to skate at Skate Days is a $2 skate rental plus an additional $3.25 for each hour Chat
you skate.
Write a function rule to represent the situation.
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Is this situation continuous or discrete? Explain your reasoning.
Create a sign that Skate Days can display at the counter that tells people how much it will cost
for each hour they skate (include 1-5 hours on your sign)
Skate City has free skate rental but charges $4 for each hour.
Which skating rink would you choose to go to?
Why did you make that choice? Use mathematical reasoning to support your answer. Lo

Answer 1

The cost is a fixed $2, plus $3.25 for any additional hour.

Then if you rent it for x hours, the cost is:

c(x) = $2 + $3.25*x

Is this situation continuous or discrete?

Yes, it is discrete, because x is "the number of hours"

so if you rent it for 1.30 hours, they will say "ok, this is equivalent to two hours".

This means that while the values of x are continuous, the possible costs are:

{$2, $2 + $3.25, $2 + 2*$3.25, ....}

Which is a discrete set.

Then the sign for 1 to 5 hours will be:

1 hour ---------- $2 + $3.25 = $5.25

2 hours -------- $2 + 2*$3.25 = $8.50

3 hours--------- $2 + 3*$3.25 = $11.75

4 hours--------- $2 + 4*$3.25 = $15

5 hours -------- $2 + 5*$3.25 = $18.25

In the other park the cost is only $4 for each hour (no fixed cost) then the total cost for x hours is:

c(x) = $4*x

Now, which option is better?

If we look at the costs for different numbers of hours for this other equation, we have:

1 hour ----- $4

2 hours ---- 2*$4 = $8

3 hours ----- 3*$4 = $12

4 hours ------ 4*$4 = $16

Then: if you want to skate 2 hours or less, Skate City is cheaper, if you want to skate more than that, kate Days is cheaper.

This happens because the first one has a smaller slope, meaning that is larger at first, but as x grows the price does not grow as much as in Skate City