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Problem 66 Hard Difficulty

An electricity company charges its customers a base rate of 10 dollars 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 \le x \le 2000 $.


$E=\$ 10+0.06 \times x$ for $x \leq 1200 \mathrm{KWh}$
$E=\$ 82+0.07 \times(x-1200)$ for $x>1200 \mathrm{KWh}$


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Video Transcript

Okay and electric company charges its customers a base rate of ten dollars a month plus six cents per kilowatt hour for the first twelve hundred kilowatts and seven cents per kilowatt hours for all Houston's over twelve hundred kilowatt hours. Express the monthly cost he as a function of the amount x of electricity used then Graff the function e for exes between zero in two thousand. Okay, so for this cost function G of X for when we use less than less than twelve hundred kilowatts, I guess we have a base rate of ten plus six cents for each kill a lot we use Okay, And then what if we use more than twelve hundred? Cure alliance. Okay, so I guess we'll have ten dollars for the base tree class. Six cents times twelve hundred. Which is gonna be Let me put that into my calculator really quick. You know your point zero six times twelve hundred, which is seventy two. So we have eighty two plus this seven cents Hercules times the amount of kill lost of use and that will be represented by X minus twelve hundred. This will be our cost function for the amount of electricity that we use okay. And to graft this maybe we'll just do a rough sketch here. You didn't color or he that of the ex. I guess we have a base rate of ten until we get twelve hundred kilowatts. So that'LL be a positive slope here, oddly enough there. And then now that's a slope of zero point zero six. Then now, after twelve hundred will have slope, that's slightly more than zero point zero six say zero point zero seven. So we'LL need to have that slightly a steeper This is just a rough sketch and then the always two thousand kilowatts.