Energy conservation

Question

to encourage engery conservation a utility company is charging its costumes a flat rate of 95 dollars per household for any electrical usage up to 1000kWh per month. Costumes who go over 1000 kWh of usage are then charged 0.151 $ for each kWh used over 1000. Writ's a function that calculates the monthly electric bill E, for any electrical usage, u. 

 

Find the E intercept for the function and interpret it's meaning. Be sure to include the units in the interpretation. 

 

Give a statement to support whether you think the E intercept is a realistic possibility, or not. 

Answer 1

To write a function, you need to think about how you would calculate you electric bill for an example number. There are actually two different ways to calculate the bill, depending on whether or not you go over the 1000kWh limit. Here's how I would think this through:

 

First, I would think about how I would calculate the bill if I did not go over the limit. I know a "flat rate" means I have to pay that amount no matter what. In this case, the flat rate is 95 dollars. So, for example, if I used 980kWh, then my bill would just be $95.

 

Second, I would think about how I would calculate the bill if I did go over the limit. Let's say I used 1,500kWh. I would still have to pay that flat rate of $95, but I would also have to pay $0.151 "for each kWh used over 1000." That means I need to figure out how much I went over by, then figure how much extra I have to pay. First I subtract: 1,500kWh -- 1,000kWh= 500kWh, to find out that I used 500 extra kWh. Then I multiply by $0.151 to see how much extra I have to pay: 500*0.151=$75.5. 

 

Finally, I would add this extra charge to the flat rate: 95 + 75.5 = 170.5.

 

To write a function, I need to go through those steps again, except this time I will use the letter "u" to represent how much electricity I used. Since there are two ways to calculate the bill depending on how much energy was used, this must be written as a piece-wise function. If the electrical usage (which we are now calling "u" is less than or equal to 1000kWh per month, then the bill is the flat rate of $95. So, 

 

E= 95,  u≤1000

 

If the electrical usage is greater than 1000kWh, then I have to add the extra fee. To find that fee, I subtracted 1000 from the electrical usage, (u) then multiplied that number by 0.151. Then I added what I got to 95. So,

 

E=(u-1000)*0.151+95, u>1000

 

You will need to write those functions together, like this:

 

E= {^{95, u≤1000}

       ^{(u-1000)*0.151+95, u>1000}

 

The y-intercept of a function is what you get for y when x is 0, so the E-intercept will be what you get for E when u is 0. If u is 0, we use the first equation, so E=$95. (make sure to include the unit,$). 

 

You would get this number for any energy usage between 0 and 1000kWh. I don't know enough about energy usage to know if this is realistically possible or not. My suggestion would be to look at an electric bill and see how much energy was used where you live in the last month. See if it is near 1000kWh or way over.

 

Hope this helps!