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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

An electricity company charges its customers a base rate of $10 a month, plus 6 cents per kilowatt-hour (kWh) for the first 1200 kWh and 7 cents per kWh for all usage over 1200 kWh. Express the monthly cost E as a function of the amount x of electricity used. Then graph the function E for 0 ≤ x ≤ 2000.

To determine

To find: The function of the monthly cost (E) in terms of an electricity used amount x and then sketch the graph of E(x) for the interval 0x2000 .

Explanation

Let the amount of electricity used be x. It is given that there is a base rate of $10 a month, plus 6 cents/kWh for the first 1200kWh. That is, the usage of electricity is less than or equal to 1200kWh, there is no change in the charge.

Therefore, if x1200kWh , then the cost function E(x) is $10+$0.06 (1)

There will be an additional charge of 7 cents/kWh other excluding $10+$0.06 , if the usage is more than 1200kMw.

Therefore, if x>1200kWh , then the cost function is,

E(x)=$10+$0.06(1200)+0.07(x1200)=$10+$72+0.07(x1200)=$82+0.07(x1200)

E(x)=$82+0

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