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Question 564187: I have attempted most of this myself however; I feel like I might have gotten a bit confused when it came to solving for 10,100,1000. This is due today! Thank you for your help!!!
An electric company charges $7.50 per month plus $0.09 for each kilowatt hour (kwh) of electricity used.
Use C as the total cost and n as the number of kwh. Write an expression that gives the total cost of n kwh of electricity.
C=7.50+0.09n
You can find the average cost per kwh by dividing total cost by number of kwh. Write the expression that gives the average cost per kwh.
C(kwh)=C/n
Find the average cost per kwh for 10 kwh, 100 kwh, and 1,000 kwh.
10 kwh You would first start by finding the overall cost
C=7.50+0.09(10)
C=7.50+0.90
C=0.84 kwh
Next plug in 0.84 for C and 10 for n.
C(kwh)=0.84/10
C(kwh)=0.084
100 kwh
C=7.50+0.09(100)
C=7.50+9
C=16.50
C(kwh)=16.50/100
C(kwh)=0.165
1000 kwh
C=7.50+0.09(1000)
C=7.50+90
C=97.50
C(kwh)=97.50/1000
C(kwh)=0.0975
As the number of kwh increases, what happens to the average cost of the kwh? Would the average cost ever fall below $0.09? If so, identify a value that supports your answer. If not, explain how you know.
As the number of kwh increases the average cost of the kwh decreases.
How many kwh should be purchased for the average cost to be $0.12 per kwh?
Found 2 solutions by scott8148, KMST:
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! your calculations for the 100 and 1000 are fine; you need to repeat the same technique from those on the 10 calculation
increasing the number of kwh lowers the average cost because the fixed cost portion of the bill ($7.50) is spread out over more kwh
the electric company charges $.09/kwh, so the average cost can never go below that value
___ the average will get closer to $.09 as the number of kwh increases and the fixed costs are spread of more kwh
$.12 = ($7.50 + $.09x) / x ___ .12x = 7.5 + .09x ___ .03x = 7.5 ___ x = 250
Answer by KMST(5328)  (Show Source):
You can put this solution on YOUR website! You were asked
Write an expression that gives the total cost of n kwh of electricity.
C=7.50+0.09n is a good answer
You were also asked
Write the expression that gives the average cost per kwh.
C(kwh)=C/n is OK, but it has two problems.
An equivalent expression was expected, and using the same letter C for the total cost and the cost per kwh is confusing.
I will use K for the average cost per kwh, and
 was the expression expected because it gives you a single expression as a function of n (no intermediate calculations).
That is expected in algebra and calculus.
I also know that was the intended answer, because all the answers to the final questions seem to come directly from there.
1) As the number of kwh increases, what happens to the average cost of the kwh? You correctly concluded that
"As the number of kwh increases the average cost of the kwh decreases."
You could conclude that from the results of the calculations
2) Would the average cost ever fall below $0.09?
Looking at as a function of n, with n being a positive real number, you see that the answer is NO.
 because 
If so, identify a value that supports your answer. Not aplicable, because it was not so.
If not, explain how you know.
 , so , and
3) How many kwh should be purchased for the average cost to be $0.12 per kwh?
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