December 3rd, 2016, 05:28 PM  #1 
Newbie Joined: Dec 2016 From: Oregon Posts: 8 Thanks: 0  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 aer midnight. Is this like asin(b(xc)+d? or acos(b(xc)+d ? If so, how do I began to extrapulate all the numbers? Thank you so much. <hisnamehere>forever 
December 3rd, 2016, 06:02 PM  #2 
Senior Member Joined: May 2016 From: USA Posts: 515 Thanks: 230 
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? 
December 3rd, 2016, 06:12 PM  #3 
Newbie Joined: Dec 2016 From: Oregon Posts: 8 Thanks: 0  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 
December 3rd, 2016, 06:30 PM  #4  
Math Team Joined: Jul 2011 From: Texas Posts: 2,287 Thanks: 1119  Quote:
 
December 4th, 2016, 04:08 PM  #5 
Newbie Joined: Dec 2016 From: Oregon Posts: 8 Thanks: 0 
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(xc)+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(xc)+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(xc)+70 Does this make sense to anyone? Last edited by HisNameForever; December 4th, 2016 at 04:19 PM. Reason: Wanted to add more info. 
December 4th, 2016, 04:17 PM  #6 
Math Team Joined: Jul 2011 From: Texas Posts: 2,287 Thanks: 1119 
$T = \dfrac{2\pi}{B} \implies B = \dfrac{2\pi}{T} = \dfrac{2\pi}{24} = \dfrac{\pi}{12}$ looks like an upsidedown cosine curve to me, with no phase shift ... agree that amplitude is $a=25$ ... vertical shift is $d = 95$ 
December 4th, 2016, 04:37 PM  #7 
Newbie Joined: Dec 2016 From: Oregon Posts: 8 Thanks: 0 
So vertical shift is always midline of the function?

December 4th, 2016, 05:18 PM  #8 
Newbie Joined: Dec 2016 From: Oregon Posts: 8 Thanks: 0  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 aer 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. 
December 4th, 2016, 05:31 PM  #9  
Math Team Joined: Jul 2011 From: Texas Posts: 2,287 Thanks: 1119  Quote:
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?  
December 4th, 2016, 05:34 PM  #10 
Newbie Joined: Dec 2016 From: Oregon Posts: 8 Thanks: 0 
I did graph my attempt. Let me check the second part. No, it doesn't add up to 120! What did I do wrong?
Last edited by HisNameForever; December 4th, 2016 at 05:46 PM. Reason: Add screen shot. 

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