1. 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)?

2. Re: Develop Piecewise Function

What is the lower bound of the domain? At what value of the domain will we switch pieces?

3. Re: Develop Piecewise Function

Originally Posted by MarkFL
What is the lower bound of the domain? At what value of the domain will we switch pieces?

4. Re: Develop Piecewise Function

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

-Dan

5. Re: Develop Piecewise Function

Originally Posted by topsquark
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.

6. Re: Develop Piecewise Function

Originally Posted by harpazo
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):

7. Re: Develop Piecewise Function

Originally Posted by MarkFL
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):

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.

8. Re: Develop Piecewise Function

Originally Posted by harpazo
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!

9. Re: Develop Piecewise Function

I start my review of basic algebra tomorrow.