Results 1 to 9 of 9
Like Tree4Thanks
  • 1 Post By MarkFL
  • 2 Post By MarkFL
  • 1 Post By harpazo

Thread: Develop Piecewise Function

  1. #1
    Super Member harpazo's Avatar
    Joined
    Sep 2014
    From
    NYC
    Posts
    995
    Thanks
    42

    Develop Piecewise Function

    In April 2009, People Energy had the following rate schedule for natural gas usage in single- family residences:

    Monthly service charge: 15.95

    Per therm service charge listed below.

    First 50 therms: 0.33606 per therm
    Over 50 therms: 0.10580 per therm
    Gas Charge: 0.3940 per therm

    Use the given information above to develop a piecewise function that relates the monthly charge C for x therms of gas.

    My Effort:

    This is tough to do. Any ideas? Any steps?

    I know that if C = charge and a function must be made, I am thinking that the needed notation is C(x).

    How do we form a piecewise function given the information above, including the side condition for each piece of C(x)?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    2,313
    Thanks
    1035

    Re: Develop Piecewise Function

    What is the lower bound of the domain? At what value of the domain will we switch pieces?
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member harpazo's Avatar
    Joined
    Sep 2014
    From
    NYC
    Posts
    995
    Thanks
    42

    Re: Develop Piecewise Function

    Quote Originally Posted by MarkFL View Post
    What is the lower bound of the domain? At what value of the domain will we switch pieces?
    This is over my head.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    11,493
    Thanks
    899
    Awards
    1

    Re: Develop Piecewise Function

    Quote Originally Posted by harpazo View Post
    This is over my head.
    What is the smallest value of C? Remember the service fee and how few therms and gas charge you could have.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member harpazo's Avatar
    Joined
    Sep 2014
    From
    NYC
    Posts
    995
    Thanks
    42

    Re: Develop Piecewise Function

    Quote Originally Posted by topsquark View Post
    What is the smallest value of C? Remember the service fee and how few therms and gas charge you could have.

    -Dan
    I've decided to return to beginning algebra. I will post beginning algebra material from now on.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    2,313
    Thanks
    1035

    Re: Develop Piecewise Function

    Quote Originally Posted by harpazo View Post
    This is over my head.
    You cannot use a negative number number of therms, so we would establish the lower bound at 0. Then we observe that at 50 therms the marginal rate, or the charge per therm changes. So, using the given information, we could write:

    $\displaystyle C(x)=\begin{cases}0.73006x+15.95, & 0\le x\le50 \\[3pt] 0.4998x + 27.463, & 50<x \\ \end{cases}$

    Here's a graph of the function (the domain of the top piece is shaded in red and the domain of the second is shaded in green, where I've added an upper bound of 150 therms):

    Develop Piecewise Function-mhf_0010.png
    Thanks from topsquark and harpazo
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member harpazo's Avatar
    Joined
    Sep 2014
    From
    NYC
    Posts
    995
    Thanks
    42

    Re: Develop Piecewise Function

    Quote Originally Posted by MarkFL View Post
    You cannot use a negative number number of therms, so we would establish the lower bound at 0. Then we observe that at 50 therms the marginal rate, or the charge per therm changes. So, using the given information, we could write:

    $\displaystyle C(x)=\begin{cases}0.73006x+15.95, & 0\le x\le50 \\[3pt] 0.4998x + 27.463, & 50<x \\ \end{cases}$

    Here's a graph of the function (the domain of the top piece is shaded in red and the domain of the second is shaded in green, where I've added an upper bound of 150 therms):

    Click image for larger version. 

Name:	mhf_0010.png 
Views:	1 
Size:	26.5 KB 
ID:	39175
    I should not be studying college algebra. I lack the needed skills. I thank you for your patience and kindness. I gotta return to beginning algebra and work my way up to college algebra.
    Thanks from DenisB
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Joined
    Feb 2015
    From
    Ottawa Ontario
    Posts
    2,255
    Thanks
    500

    Re: Develop Piecewise Function

    Quote Originally Posted by harpazo View Post
    I should not be studying college algebra. I lack the needed skills. I thank you for your patience and kindness. I gotta return to beginning algebra and work my way up to college algebra.
    Heck of a good plan. That's the way we all did it!
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Super Member harpazo's Avatar
    Joined
    Sep 2014
    From
    NYC
    Posts
    995
    Thanks
    42

    Re: Develop Piecewise Function

    I start my review of basic algebra tomorrow.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 14
    Last Post: Oct 7th 2011, 09:45 PM
  2. Piecewise function
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Nov 17th 2010, 10:51 AM
  3. Replies: 2
    Last Post: Sep 26th 2010, 06:00 PM
  4. Replies: 3
    Last Post: Jun 4th 2010, 10:40 PM
  5. piecewise function
    Posted in the Calculus Forum
    Replies: 5
    Last Post: Aug 10th 2009, 12:05 AM

/mathhelpforum @mathhelpforum