Question

at an airport it costs $7 to park for up to one hour and $5 per hour for each additional hour. let x represent the number of hours parked. write the function that modles the cost, C(x), of the parking x hours, where x is an integer greater then 1.

Answer 1

C(X) = 7 + 5(X-1)

Explanation:

So, the cost for parking from 0 to 1 hour is $7. Then, for one extra hour, from 1 to 2, you have to pay an additional $5. For another hour, from 2 to 3, an extra $5, and so on. So, lets make a quick table:

Hours Cost

[0-1] $7

(1-2] $7+$5

(2-3] $7+$5+$5

(3-4] $7+$5+$5+$5

So, for 1 hour the cost is $7, for 2 hours $12, 3 hours $17, 4 hours $22, and so on. We can see a pattern here: the cost for X hours is $7 plus $5 for each hour greater than 1. So we can write the cost function as:

C(X) = 7 + 5(X-1)

If X=2, 2 hours, the cost is:

C(2) = 7 + 5(2-1) = 7 + 5 = 12, so the function fits.

Notice that here I used the parenthesis in a (--] form, however, it could also be used in a [--) form. If the last is chosen, 2 hours would cost $17 instead of $12. The function would be C(X) = 7 + 5X.

As the statement does not specifies, any of this ways can be used.