  The monthly charge in dollars for x kilowatt-hours (kWh) of electricity used by a residential consumer of an electric company from November through June is given by the function below.C(x) =20 + 0.188x if 0 ≤ x ≤ 10038.80 + 0.15(x − 100) if 100 < x ≤ 50098.80 + 0.40(x − 500) if x > 500(a) What is the monthly charge if 1800 kWh of electricity is consumed in a month?

Question

The monthly charge in dollars for x kilowatt-hours (kWh) of electricity used by a residential consumer of an electric company from November through June is given by the function below.
C(x) =

20 + 0.188x if 0 ≤ x ≤ 100
38.80 + 0.15(x − 100) if 100 < x ≤ 500
98.80 + 0.40(x − 500) if x > 500
(a) What is the monthly charge if 1800 kWh of electricity is consumed in a month?

Step 1

The monthly charge in dollars for x kilowatt-hours (kWh) of electricity used by a residential consumer of an electric company from November through June is given by the function below.
C(x) =

(a) 20 + 0.188x if 0 ≤ x ≤ 100
(b) 38.80 + 0.15(x − 100) if 100 < x ≤ 500
(c) 98.80 + 0.40(x − 500) if x > 500

I have assigned (a), (b) & (c) to the three branches of the function so that we can refer to them easily, subsequently.

Step 2

If 1800 kWh of electricity is consumed in a month, then x = 1,800 for that month.

x = 1,800 lies in the branch (c) of the function as x = 1,800 > 500

Step 3

As per branch (c):

The monthly charge in dollars for x kilowatt-hours (kWh) of electricity us...

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