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December 3rd, 2016, 05:28 PM   #1
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Periodic Function

Hey Forum People,

I am doing practice problems for a final. I have a problem finding a function for
The amount of electrical power a town consumes at a given time of day is roughly periodic. Hoping someone can get me started on this one. Thanks a lot. Here's the problem.

Assuming a city's power consumption reaches a peak value of 120 MW (megawatts) at noon, and reaches a minimum value of 70 MW over night, find a function p(t) which will approximate the city’s power consumption t hours a‰er midnight.

Is this like asin(b(x-c)+d? or acos(b(x-c)+d ? If so, how do I began to extrapulate all the numbers? Thank you so much.

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December 3rd, 2016, 06:02 PM   #2
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Hint 1: Measure time in hours after midnight.

Hint 2: What is t when is consumption is least?

Hint 3: What is t when consumption is highest.

Hint 4: What functions do you know that are periodic?

Hint 5: Why might the midpoint of 120 and 70 be a relevant number?
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December 3rd, 2016, 06:12 PM   #3
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Periodic Function

Thank you Jeff, I'll work from that and start a function. I know that sine and cosine are periodic, so I will try your hints. I don't have solutions to these yet, but I probably will before the final. I'll post back if I solve it or continue to have trouble. Obvously, you gave me everything I need to know. I will have to go through the hints carefully with the problem. Thanks again.

-Steve
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December 3rd, 2016, 06:30 PM   #4
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Quote:
Assuming a city's power consumption reaches a peak value of 120 MW (megawatts) at noon, and reaches a minimum value of 70 MW over night, find a function p(t) which will approximate the city’s power consumption t hours after midnight.
I'd start by making a sketch of power in MW vs. time in hours with a period of 24 hours ...

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December 4th, 2016, 04:08 PM   #5
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That's exactly what I did. I got the same graph you did. I have the Amplitude at 25 and this seems to make my function start out as:

f(t)=25sin(b(x-c)+d
,
right? I know it's simple but I don't know how to get the rest from what I'm given. I know the Period =1/B or 2pi/B. It looks to me like my period is 24. So maybe I have:

f(t)=25sin(24(x-c)+d.

I'm not sure where to go from here. Maybe someone could help.

<edit>

Maybe if Period=2pi/b, and my period is 24 then b=2pi/24=pi/12. If d is vertical shift then maybe I have so far:

f(t)=25sin(pi/12(x-c)+70

Does this make sense to anyone?

Last edited by HisNameForever; December 4th, 2016 at 04:19 PM. Reason: Wanted to add more info.
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December 4th, 2016, 04:17 PM   #6
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$T = \dfrac{2\pi}{B} \implies B = \dfrac{2\pi}{T} = \dfrac{2\pi}{24} = \dfrac{\pi}{12}$

looks like an upside-down cosine curve to me, with no phase shift ...

agree that amplitude is $a=25$ ... vertical shift is $d = 95$
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December 4th, 2016, 04:37 PM   #7
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So vertical shift is always midline of the function?
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December 4th, 2016, 05:18 PM   #8
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Solution Follows

For this problem:

Assuming a city's power consumption reaches a peak value of 120 MW (megawatts) at noon, and reaches a minimum value of 70 MW over night, find a function p(t) which will approximate the city’s power consumption t hours a‰er midnight.

P(t)=25sin(pi/12(t+24)+95

If I graph that I get a function that graphs the power consumption of the city in the problem above. Yay! Thanks everyone for the help.

Last edited by HisNameForever; December 4th, 2016 at 05:34 PM.
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December 4th, 2016, 05:31 PM   #9
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Quote:
Originally Posted by HisNameForever View Post
For this problem:

Assuming a city's power consumption reaches a peak value of 120 MW (megawatts) at noon, and reaches a minimum value of 70 MW over night, find a function p(t) which will approximate the city’s power consumption t hours a‰er midnight.

P(t)=25sin(pi/12(x+24)+95

If I graph that I get a function that graphs the power consumption of the city in the problem above. Yay! Thanks everyone for the help.
first, I think you meant to type ...

P(t)=25sin(pi/12(t+24))+95

so, given that function you came up with ... does P(12) = 120 as stated in the problem?

did you graph your attempt?
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December 4th, 2016, 05:34 PM   #10
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I did graph my attempt. Let me check the second part. No, it doesn't add up to 120! What did I do wrong?
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Last edited by HisNameForever; December 4th, 2016 at 05:46 PM. Reason: Add screen shot.
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