The table shows the populations P (in millions) of Georgia,...

The table shows the populations $ P $ (in millions) of Georgia, New Jersey,and North Carolina from $ 2002 $ through $ 2007 $.(Source:U.S. Census Bureau) (a) Use the regression feature of a graphing utility to find linear models for each set of data. Let $ t $ represent the year, with $ t = 2 $ corresponding to $ 2002 $. (b) Use a graphing utility to graph the data and the models in the same viewing window. (c) Use the graph from part (b) to approximate any points of intersection of the graphs of the models.Interpret the points of intersection in the context of the problem. (d) Verify your answers from part (c) algebraically.

The table shows the populations $ P $ (in millions) of Georgia, New Jersey,and North Carolina from $ 2002 $ through $ 2007 $.(Source:U.S. Census Bureau)

(a) Use the regression feature of a graphing utility to find linear models for each set of data. Let $ t $ represent the year, with $ t = 2 $ corresponding to $ 2002 $.

(b) Use a graphing utility to graph the data and the models in the same viewing window.

(c) Use the graph from part (b) to approximate any points of intersection of the graphs of the models.Interpret the points of intersection in the context of the problem.

(d) Verify your answers from part (c) algebraically.

Transcript

00:01 Okay, for number 76, we've got multiple parts, but a lot of them are do it on the calculator, tight moments, right? so let's go ahead and just sort of check through.

00:11 We've got a table that shows the populations of a couple of three states.

00:16 So we're going to use the regression feature to find linear models for each of those growth, population growth, and then we're going to graph the data and the models at the same time in the viewing window.

00:30 And then we're going to find the points of intersection.

00:32 So we got to do all those things first.

00:34 Over here on the t -i -89, here is what they all look like.

00:38 I went ahead and graphed them all, right? so how did i do this? i had to go to the apps, and they had to say data matrix editor, and then type in all the data, right? i typed it into all those columns.

00:53 Then for each one, i had to do an f -5 calculation and say, i want to do a linear regression, right? and then i would say, well, okay, what's your x, what's your y? and so you type in c1 and c2, then c1, c4, you have to do each one of the time, right? and then you're storing it over here to y1, y2, and y3.

01:18 So you have to pick a different one for each one of these.

01:23 Okay? all right.

01:24 So i'm going to go ahead and escape from this because i've already done that.

01:27 And when you set up the actual plots, this is the other part that makes it look really, really good, is you can do like the plot setup.

01:35 And then i have defined each one of these.

01:38 Okay.

01:39 So i went ahead and for each one of my plots, i was able to say what i wanted it to look like in terms of what the data points were.

01:46 Okay.

01:46 This is how you make the data points show up.

01:48 Otherwise, if they're undefined, they're just blank.

01:51 Okay.

01:52 So, you know, you go into f1 and you can describe it right there.

01:56 And you can say this is my c1, c4, so go ahead and do a scatter plot, mark it with a square, et cetera.

02:03 Okay, so i'm going to go ahead and escape this because i have already done that as well.

02:07 So then when you graph it, it usually looks beautiful.

02:10 If you have an issue and it doesn't seem to be graphing, right, you can always do a zoom.

02:15 Go all the way down to nine and say zoom data, right? and then that'll put it right there on the middle for you.

02:21 It kind of centers it up.

02:23 All right.

02:24 Next, we have to find our intersections.

02:26 It says use the graph to do it.

02:28 So you can do it on the calculator fairly easily.

02:30 You can say f5 math, and you can say intersection.

02:34 And it has to ask you which one is the first curve.

02:36 These are lines.

02:37 But okay, sure, it's that one.

02:40 We can't tell which one we're talking about here...

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