Question 1208092: In the summer of 2009,Duke Energy supplied electricity to residences of Ohio for amonthly customer charge of $4.50 plus 4.2345¢ per kilowatt-hour (kWhr) for thefirst 1000 kWhr supplied in the month and 5.3622¢ per kWhr for all usage over 1000 kWhr in the month.
If C is the monthly charge for x kilowatt-hours, write a model relating charge and
kilowatt-hours used. That is, write C as a function of x.
I know that our equation model begins with C(x) = something + something else in terms of x.
Here is what the textbook tells me.
The model can be found by multiplying x times $0.042345 and adding the montgly customer charge of $4.50.
The model is C(x) = $4.50 + x(0.042345).
Question:
Where did $0.042345 come from?
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website!
The model is C(x) = $4.50 + x(0.042345).
4.50 is dollars
4.2345 is in cents.
4.2345 cents is converted to dollars dividing by 100
Answer by ikleyn(52879)  (Show Source):
You can put this solution on YOUR website! .
The solution in the post by @mananth is incomplete.
The complete solution should be, OBVIOUSLY, a piecewise linear function C(x)
with one formula for 0 <= x <= 1000 kilowatts-hours and another formula for x > 1000 kilowatt-hours.
For 0 <= x <= 1000 kWh, the formula is
C(x) = 4.50 + 0.042345x dollars (rounded to the closest cent).
At x = 1000 kWh, it gives C(1000) = 4.50 + 0.042345*1000 = 46.845 dollars before rounding,
or = 46.85 dollars after rounding.
For x > 1000 kWh, the formula is
C(x) = 46.85 + 0.053622*(x-1000) dollars (rounded to the closest cent).
It is a complete solution to the problem.
Solved in full, with complete explanations.
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When you ask where the coefficients come from, this is a completely childish
question - it does not correspond to the level of the problem.
The level of the problem is about 9-th grade.
The level of the question "where the coefficients come from" is about 3-rd or 4-th grade.
So, you try to solve a problem of the 9-th grade without having solid base/knowledge of the 4-th grade.
It is what I see from your post.
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