[MOVED] Finding a Formula for airport-parking charge

[Johnwill]

Question: Valuepark charge $1.10 per hour fraction hour airport parking. The maximum charge per day is $7.25.

(a) Write a formula that gives the charge for x hours with 0 <= x <= 24

(b) Graph the function in a and at what values of x is it continous.

what i know so far from this question is that the price shouldn't exceed $7.25, so does this mean that after a certain number of hours the price will be $7.25, no matter how many hours you park for that day?

Valuepark charge $1.10 per hour or fraction hour for airport parking. The maximum charge per day is $7.25.

(a) Write a formula modelling the charge for x hours, where 0 < x <24

(b) Graph the function in part (a) and list the x-values at which the function is continuous

 

[stapel]

This question is very badly written. Let's do some clarification first.

Valuepark charge $1.10 per hour fraction hour airport parking.

Are we assuming that this means "Valuepark charges $1.10 per hour or fraction of an hour for airport parking"?

(a) Write a formula that gives the charge for x hours with 0 <= x <= 24

"Write a formula modelling the charge for x hours, where 0 < x <24"?

(b) Graph the function in a and at what values of x is it continous.

"Graph the function in part (a) and list the x-values at which the function is continuous"?

what i know so far from this question is that the price shouldn't exceed $7.25

The daily price does not exceed $7.25. However, if you park, say, for three full days, then the total price will exceed $7.25.

does this mean that after a certain number of hours the price will be $7.25

Yes; the listed daily maximum is the maximum that can be charged for one day.

Thank you.

Eliz.

 

[Johnwill]

this was given directly from a book i was using... .. and it's $7.25 daily. that's why i wrote

Valuepark charge $1.10 per hour fraction hour airport parking.

Are we assuming that this means "Valuepark charges $1.10 per hour or fraction of an hour for airport parking"?

yes, ur right it's per hour or fraction of an hour..sorry for my typo.

The daily price does not exceed $7.25. However, if you park, say, for three full days, then the total price will exceed $7.25.

i thought that the maximum price for a day is $7.25, so could you help me what does $1.10 per hour or fraction of an hour for airport parking mean?

 

[stapel]

i thought that the maximum price for a day is $7.25, so could you help me what does $1.10 per hour or fraction of an hour for airport parking mean?

It means exactly what it says: For each hour (or fractional part of an hour), you pay $1.10 per hour. This is like the charges for stamps: For each ounce, or portion thereof, you need one stamp. You can't say that your package only weighs half an ounce, so you don't have to pay; or that your package only weight 1.8 ounces, so you only need one stamp. Any ounce, or fractional part, requires one stamp.

Then, if/when the charges get high enough, you stop adding $1.10 for each additional hour (or fractional part thereof), and cap the day's charges at $7.25.

Then you start over again the next day.

Eliz.

 

[Johnwill]

oh, now i understand, so it's like this:

even if you park for 15 minutes you have to pay!!.., could you give me some hints with the formula

the thing i am stuck at is that what should i to when the amount exceeds $7.25

 

[stapel]

could you give me some hints with the formula

How much would you pay for any time up to the first hour? How much would you pay for any time up to the second hour?

Keep going until you see a pattern that can be turned into a formula. (I don't know what you've been studying lately in class, but a "greatest integer" function or a piecewise function is probably what is being looked for here. Check your text and/or your class notes for relevant examples.)

the thing i am stuck at is that what should i to when the amount exceeds $7.25

But... it won't exceed $7.25. That's the point of $7.25 being the "maximum charge per day": the charge won't go any higher.

Eliz.

 

[Johnwill]

could you give me some hints with the formula

How much would you pay for any time up to the first hour? How much would you pay for any time up to the second hour?

Keep going until you see a pattern that can be turned into a formula. (I don't know what you've been studying lately in class, but a "greatest integer" function or a piecewise function is probably what is being looked for here. Check your text and/or your class notes for relevant examples.)

the thing i am stuck at is that what should i to when the amount exceeds $7.25

But... it won't exceed $7.25. That's the point of $7.25 being the "maximum charge per day": the charge won't go any higher.

Eliz.

thanks eliz, i think it's peicewise function too

what i have found so far is that after 6 hours I gotta pay $6.6 ($1.1 * 6)

but in the 7th hour i exceed the per day amount

so is the equation going to look like:

f(x) = {1.1x 1<x<6
but the problem i got now is that the question askes the formula for x hours between 0 and 24

 

[stapel]

but the problem i got now is that the question askes the formula for x hours between 0 and 24

You (sort of) have an expression for the values between zero and six. Now, what happens at x = 7? What value do you get for x = 8? For x = 10? x = 15?

The "formula" for 6 < x < 24 is fairly simple.

Eliz.

 

[Johnwill]

but the problem i got now is that the question askes the formula for x hours between 0 and 24

You (sort of) have an expression for the values between zero and six. Now, what happens at x = 7? What value do you get for x = 8? For x = 10? x = 15?

The "formula" for 6 < x < 24 is fairly simple.

Eliz.

I think it's:
f(x)= 7.25

so, are these the two equations that i'm supposed to graph?


when x =7 you have to pay $7.70 which exceeds the per day fee


how will i know which values will be continuous

is it 0-6 and 6-24?