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Numerade Educator

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Problem 15 Easy Difficulty

The graph shows the power consumption for a day in September in San Francisco. ( $ P $ is measured in megawatts; $ t $ is measured in hours starting at midnight.)

(a) What was the power consumption at 6 am? At 6 pm?
(b) When was the power consumption the lowest? When was it the highest? Do these times seem reasonable?

Answer

(a) The power consumption at 6 AM is $500 \mathrm{MW}$, which is obtained by reading the value of power $P$ when $t=6$ from the graph At 6 PM we read the value of $P$ when $t=18$, obtaining approximately 730 MW.
(b) The minimum power consumption is determined by finding the time for the lowest point on the graph, $t=4,$ or 4 AM. The maximum power consumption corresponds to the highest point on the graph, which occurs just before $t=12,$ or right before noon. These times are reasonable, considering the power consumption schedules of most individuals and businesses.

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Video Transcript

Okay. The graph shows the power consumption for a day in September in San Francisco. Piece measured in big watch case in hours starting at midnight. And so for this first question here, eh, What is the power consumption at six a. M. And at six. PM? Okay, so at six. A. M. It looks like that will be, you know, burst six hours here. That will be a five hundred megawatts. Okay. Looks like we consume five hundred megawatts there and then at six. P. M. You know? Well, if your were all you Peter Science majors will know about modular arithmetic. Eighteen is a six more twelve there. So, you know, eighteen the clock will be at about seven hundred. We're using seven hundred megawatts, Karen. And for B one, Was the power consumption the lowest? When was it at the highest? You these times seem reasonable. So at its slowest, it's going to be about, you know, somewhere between three. And four PM or three. And four a m. Yeah, in it's highest. We'LL be around twelve. One o'Clock. Okay. And so yeah, those times do makes sense because I'm usually a sweep around three to four hand, so I must be using least amount of power consumption. Okay. And probably the most awake at around twelve or one, just because I work at the signs having lunch, doing really good there.