# nonlinear prices

• Aug 1st 2009, 11:42 AM
gertlers10
nonlinear prices
I know this has got to be really easy but I'm on summer vacation and I'm blanking-

If a service charges

$15 for 30min and$25 for 1 hour

What is a function of time that will give me those values and everything inbetween?
• Aug 1st 2009, 12:56 PM
stapel
Convert the second point from "hours" to "minutes", so you have the same units.

Then use the fact that they've given you two points in the form (x, y) = (minutes, cost), along with the formula for slope to find the slope of the line through these two points.

Then take one of the points (it doesn't matter which) and the slope you just found, and plug them into one of the straight-line formulas, such as the point-slope formula, to find the equation of the straight line through these two points.

If you get stuck, please reply showing how far you have gotten. Thank you! (Wink)
• Aug 1st 2009, 12:58 PM
VonNemo19
Quote:

Originally Posted by gertlers10
I know this has got to be really easy but I'm on summer vacation and I'm blanking-

If a service charges

$15 for 30min and$25 for 1 hour

What is a function of time that will give me those values and everything inbetween?

Not quite sure what you're asking, but...

This is a stepwise function, meaning that everytime a customer exceeds the time limit he/she has to pay for an additional time period even if only for a moment.

These functions are denoted by

$\displaystyle C(t)=[[t]]$

http://www.ehow.com/video_4756977_us...-function.html
• Aug 1st 2009, 01:54 PM
gertlers10
Quote:

Originally Posted by stapel
Convert the second point from "hours" to "minutes", so you have the same units.

Then use the fact that they've given you two points in the form (x, y) = (minutes, cost), along with the formula for slope to find the slope of the line through these two points.

Then take one of the points (it doesn't matter which) and the slope you just found, and plug them into one of the straight-line formulas, such as the point-slope formula, to find the equation of the straight line through these two points.

If you get stuck, please reply showing how far you have gotten. Thank you! (Wink)

No, see it's not a linear function because at 0 time there should be 0 charge. I have three points:

(0,0)
(.5,15)
(1,25)

Now I need an equation to satisfy that.
• Aug 1st 2009, 01:59 PM
VonNemo19
In your original post, it was implied that the charges were to be by the half hour, or by the hour respectively. In most real world applications (Eg: postage, rentals, etc.) this means that there are no "in between" charges. You either pay for an hour (or half-hour) or nothing at all. If this is the case, see my last post and then tell me if there is something that you do not understand. If it is not the case, again, tell me and I will adjust my approach accordingly.
• Aug 1st 2009, 02:41 PM
gertlers10
Quote:

Originally Posted by VonNemo19
In your original post, it was implied that the charges were to be by the half hour, or by the hour respectively. In most real world applications (Eg: postage, rentals, etc.) this means that there are no "in between" charges. You either pay for an hour (or half-hour) or nothing at all. If this is the case, see my last post and then tell me if there is something that you do not understand. If it is not the case, again, tell me and I will adjust my approach accordingly.

Okay, then forget about it being real world application. I just want a function that goes through:
(0,0) (.5,15) (1,25)

what do I do?
• Aug 1st 2009, 02:48 PM
yeongil
nm
• Aug 1st 2009, 02:53 PM
gertlers10
Quote:

Originally Posted by yeongil
Where in the problem does it say that there is no charge for 0 minutes? It's possible to have a charge for 0 minutes. One could express something like, "a service charges x dollars, plus y dollars per hour."

You're not going to get a linear equation that will satisfy this, because the slope between the 1st two points and the slope between the last two points aren't the same.

Taking the (0, 0) point out, find the slope between (.5, 15) and (1, 25), using the formula
$\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}$.

Then plug in m, and plug in either of the points for x & y, into the slope-intercept form
$\displaystyle y = mx + b$
to solve for b. (Incidentally, b tells how the service charge for 0 minutes.)

01

I DONT WANT A LINEAR EQUATION! read the the title!!

Ha. I don't mean to yell, I know you are just trying to help.

I made this problem up. I want a nonlinear equation. Quadratic or exponentional or whatever, I just can't remember what to do.
• Aug 1st 2009, 03:06 PM
VonNemo19
Quote:

Originally Posted by gertlers10
I DONT WANT A LINEAR EQUATION! read the the title!!

Ha. I don't mean to yell, I know you are just trying to help.

I made this problem up. I want a nonlinear equation. Quadratic or exponentional or whatever, I just can't remember what to do.

Familiarize yourself with regression, and you should be all set.

Next time, Express exacly what is that you need help with. Every one here has tried as hard as they can to help you. If you'd like to improve your chances of getting the help that you need, start clicking the "thanks" button, instead of overheating.
• Aug 2nd 2009, 09:44 AM
stapel
Quote:

Originally Posted by gertlers10
I want a nonlinear equation. Quadratic or exponentional or whatever....

Well, which one did you want? A quadratic, an exponential, or something else?

We can't see the data you're looking at, and we can't know the patterns you have or need. There are infinitely-many equations which can be put through the listed points (two originally, and now three). You'll need to specify what you're expected to find, what techniques you've been directed to use, and where you're getting stuck.

Thank you! (Wink)