Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,637

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

---

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

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

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?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,637

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

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

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 mathxyz (2024-04-14 10:21:33)

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

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?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,637

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

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

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.