Math Is Fun Forum

nycguitarguy

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 566

Develop A Math Model

In April 2009, Nicole Gas had the following rare schedule for natural gas usage in single-family residences:

Monthly customer charge = $8.40

Distribution charge

1st 20 therms = $0.1473 per therm
Next 30 therms = $0.0579 per therm
Over 50 therms = $0.0519 per therm

Gas supply charge = $0.43 per therm

Develop a math model that gives the monthly charge C for x therms of gas.

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The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.

Dr. David Jeremiah

Bob

Administrator

Registered: 2010-06-20

Posts: 10,208

Re: Develop A Math Model

if x represents the number of therms used you have to create a piecewise definition like this

0 < x ≤ 20 C = 8.40 + 0.1473x + 0.43x

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

nycguitarguy

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 566

Re: Develop A Math Model

if x represents the number of therms used you have to create a piecewise definition like this

0 < x ≤ 20 C = 8.40 + 0.1473x + 0.43x

Bob

Is that the correct function?

If so, how did you do that, Bob?

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The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.

Dr. David Jeremiah

Bob

Administrator

Registered: 2010-06-20

Posts: 10,208

Re: Develop A Math Model

I think so. The cost is made up from a monthly charge, a distribution charge and a supply charge.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

nycguitarguy

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 566

Re: Develop A Math Model

I think so. The cost is made up from a monthly charge, a distribution charge and a supply charge.

Bob

Your function C is linear. I will continue trying to figure this piecewise function to the best of my ability.

Last edited by nycguitarguy (2024-04-14 10:21:33)

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The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.

Dr. David Jeremiah

nycguitarguy

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 566

Re: Develop A Math Model

I think so. The cost is made up from a monthly charge, a distribution charge and a supply charge.

Bob

Bob,

I needed to post the entire question to make sense of it all.

A. What is the charge for using 40 therms in a month?

I need to find decimal value for 40 therms.

I will set up a proportion.

Let x = decimal value for 40 therms.

20/40 = 0.1473/(x)

Solving for x, I get 0.2946 per therm for 40 therms.

To answer A, 40(0.2946) = $11.784

B. What I the charge for using 150 therms in a month?

For this, I need to use my answer in A plus 150(0.0519) = $13.677.

I think my piecewise function is set up this way:

C(x) = 4.50 + 0.1473x if x <= 20...top portion

C(x) = 4.50 + 40(0.1473) + 0.0519x if x > 50...bottom portion

You say?

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The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.

Dr. David Jeremiah

Bob

Administrator

Registered: 2010-06-20

Posts: 10,208

Re: Develop A Math Model

There is one fixed charge whatever the amount used:  Monthly customer charge = $8.40

Then there's a charge that has a variable rate depending on how much you use.

You have to start by charging for the  first 20 therms at the first rate.

Distribution charge

1st 20 therms = $0.1473 per therm

Then, if 40 are used altogether, you've still got to pay for another 20 (40-20) at the next rate.

Next 30 therms = $0.0579 per therm

Nothing to pay at the third rate as all therms have been accounted for.

Over 50 therms = $0.0519 per therm

Then there's a Gas supply charge = $0.43 per therm which semms to be at a single rate whatever the amount of therms, so you need to pay for 40 at 0.43

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

nycguitarguy

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 566

Re: Develop A Math Model

There is one fixed charge whatever the amount used:  Monthly customer charge = $8.40

Then there's a charge that has a variable rate depending on how much you use.

You have to start by charging for the  first 20 therms at the first rate.

Distribution charge

1st 20 therms = $0.1473 per therm

Then, if 40 are used altogether, you've still got to pay for another 20 (40-20) at the next rate.

Next 30 therms = $0.0579 per therm

Nothing to pay at the third rate as all therms have been accounted for.

Over 50 therms = $0.0519 per therm

Then there's a Gas supply charge = $0.43 per therm which semms to be at a single rate whatever the amount of therms, so you need to pay for 40 at 0.43

Bob

Bob,

I did the best I could. This is not an easy question. It takes lots of practice that I simply have little time for. I am also in the process of starting a new job. A lot of stuff on my plate right now.

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The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.

Dr. David Jeremiah