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# Periodicity of algebraic models

CCSS.Math:

## Video transcript

we're told Divya is seated on a ferris wheel at time T equals zero the graph below shows her height H in meters T seconds after the ride starts so at time equals zero she is looks like about two what is this this would be one and a half so it looks like she's about to two meters off the ground and then as time increases she gets as high as it looks like this is close to 30 maybe 34 meters and then she comes back down back to looks like two meters and up two to be 34 meters again so let's read the question so the question asks us approximately how long does it take Divya to complete one revolution on the ferris wheel alright so this is interesting so this is when she's at the bottom of the ferris wheel so then she gets to the top of the ferris wheel and then she keeps rotating until she gets back to the bottom of the ferris wheel again so it took her six T and T is in terms of seconds so it took her 60 seconds to go from the bottom to the bottom again another 60 seconds she would have completed another revolution and so let me fill that in it is going to take her 60 seconds 60 seconds and we of course can check our answer if we like let's do another one of these so here we have a doctor observes the electrical activity of Finn's heart over a period of time the electrical activity of Finn's heart's heart is cyclical as we hope it would be and it Peaks every 0.9 seconds which of the following graphs could model a situation if T stands for time in seconds and E stands for the electrical activity of Finn's heart in volts well over here looks like we peaked at zero seconds and then here we're picking a little bit more than one this looks like maybe at one point one now maybe at two point two and three point three this looks like it's speaking a little bit more than every one second so like maybe every 1.1 seconds not every zero point nine seconds so I'd rule out a this one is peaking it looks like the interval between Peaks is less than a second but looks like a good business in a second so it looks like maybe every three quarters a second or maybe every four-fifths of a second not quite nine-tenths nine-tenths this first peak would be a little bit closer to one but this one is close choice C is looking good the first we're at zero then the first peak this looks pretty close to one was less than one it looks like a tenth less than one so I like choice C that choice D it looks like we're peaking every half second so it's definitely not bad so this looks like a peak of every 0.9 seconds this is the best representation that I this is the best representation that I can think of and you can you can actually verify that you have a peak every every 0.9 seconds you're gonna have four peaks in 3.6 seconds so one two three four this is it this looks like it's at three point six over here you have one two three four you've had four peaks in less than three seconds so this definitely one this one definitely isn't 0.9 so instead of just even forcing yourself to eyeball just between the this peak and that peak you can say well if for every point nine seconds how long would three peaks take or four peaks and then you can actually a little bit more precise as you try to eyeball it so we can check our answer and verify that we got it right