SOLUTION: 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 sup

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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(52855)   (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.


/////////////////////


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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