Hey, there were doing problem number 17. Um, in 17. They give us a bunch of numbers here, and they talk about the population of Wyoming s. Oh, we've got some data, and we have to perform some tasks. Um, they're asking us to use a graphing utility thio create a scatter plot. Then they went D five equal 2005 data. So I've gone ahead and enter the information here on the T I 89 calculated may be different. Or you could use a website. There's lots of websites out there that are very, very similar to this. Um, anyway, and so I'm gonna go ahead and run some the new regression on it. So that could tell us what the best fit line is to match this data on this. I do f five, and then I go ahead and set it up. So it says linear regression. And then I'm gonna go ahead and tell it where to find the data, which is in see one and C two, and I'm going to tell it to save that equation into the graph for so that we can find it and look at it. Why one great place for it. All right, we're ready to roll. Intern. All right, This is the full version of our A and B, and you'll notice that put the equation for a line up there so that we can see it. Um, if we're writing the equation, we could put these ones in. Okay, Um uh ah. Linear model of the data would include this. We could use rounded versions if you wanted to. Let's go ahead. And, uh, we created our scatter plot, and we found the model for the data. Let's go ahead and right this in, shall we? Okay, this is the equation, and it's again, it's sort of it's rounded form. Um, next, we're gonna get back over here, and let's take a look at what this is. They want to step, model and put the model and the data points all in one, which we could do fairly easily. Uh, let's enter here and then remember, I sent it over to the graph. So if your graph looks like this, you probably need to zoom. My favorite zoom is number nine zoom data. Whoa. Okay, this is good, because this is different than the other problems. Um, is the model a good fit? Well, you know, it ain't too good. It just doesn't look very good to me. What it looks like is I've got a clear sort of parabolic growth curve. It goes up and down again, and I'm trying to model that using a line. So unfortunately, I'm gonna have to say that. No, it doesn't look like a very good fit. It all, um I want Yeah, because it it looks like it's not really the right shape to be using it. So I'm gonna say no, it doesn't fit the data. No, comma, it doesn't fit the data. The data doesn't look like a line. Right? Okay. And then I'm in for D. They ask us to predict the population of Wyoming when it's the year 2050. I've got some family in Wyoming, so let's see, in 2050 what will that be? We could substitute back in 2050. We used 50 instead of 2050 for our X value here. T I guess it probably should be. I wouldn't change it to to you while I'm here just because it's time. And they asked for tea. E like that better t But we can also go back to our calculator. And since this is in the graph, are already we can just look at the table view, which gives us all the results, just those numbers that it's calculated already for us. So we don't have to necessarily go through the entire solving the equation by hand. We already did solve the equation for all numbers because we entered it in here and got a model. So it's asking for what, 2050? So that would correspond to 50. That would be right there. 543.43 by those people. I've 43.43 now. This is in thousands said eso the actual population people would be 543,000 comma, comma, 430 people. I like to go and fill this out all the way. People in 2050. Okay, so does the results seem reasonable and explain This is probably the toughest part. So for D Okay, when we're looking at this, I was already saying that I didn't like the way that this sort of curve was modeled using the line. Um, the way that the trend is going. If we were to extrapolated just, you know, imagining where the next data point would be, we would think it would be lower than the value for the line. And indeed, in 2050 this number is higher, like it's a growing population. But if it actually does sort of follow this curve, 2050 might be way down there, and then we might be way off. You understand what I'm saying? I mean, this is probably a more accurate like representation. If I just do a curve, it would go with the data better. Okay, so in this case, yeah, it's like 10 kinds of messed up. How will we phrase that there's results seem reasonable? I'll say, given the data. No, it doesn't s. So you don't have to watch me right when deposit. Okay, So given the data trend, it doesn't seem reasonable that it would be increasing. Now we know the populations increase over time. We know that, um, but if you've ever been to Wyoming, sometimes Wyoming hasn't issues. It's like there's just not a whole lot of people, and the population could very easily go up for some reason, and then decrease for some reason. Um, so in my opinion, it does not seem reasonable, but these were only predictions, so I mean, you know, most populations grow, so that part seems reasonable. It's a little bit of both. Honestly, All right. And that Make sure we check that off. Yes, and that's the end.