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Point) Gct help entcring onswcrtWorld milk production rose at approximately constant rate between 1997 and 2003_ See the figure below:n(hillion tonc)tuears #ince 19...

Question

Point) Gct help entcring onswcrtWorld milk production rose at approximately constant rate between 1997 and 2003_ See the figure below:n(hillion tonc)tuears #ince 1997)(You can click on the graph to enlarge the image )Which formula is the best one to approximate the milk production; M (million tons) , as a function of (years since 1997)?A. M 352 + 1O(t _ 1997) 3. M = 337 + 10t C.M = 337 _ 2t D. M = 337 + I0(t _ 1997) EM = 352 2(t _ 1997) EM = 352 + 10t G.M = 352 - 2t H.M = 337 _ 2(t - 1997)Refere

point) Gct help entcring onswcrt World milk production rose at approximately constant rate between 1997 and 2003_ See the figure below: n(hillion tonc) tuears #ince 1997) (You can click on the graph to enlarge the image ) Which formula is the best one to approximate the milk production; M (million tons) , as a function of (years since 1997)? A. M 352 + 1O(t _ 1997) 3. M = 337 + 10t C.M = 337 _ 2t D. M = 337 + I0(t _ 1997) EM = 352 2(t _ 1997) EM = 352 + 10t G.M = 352 - 2t H.M = 337 _ 2(t - 1997) Reference: Based on Statistical Abstracts of the US 2004-2005, Table



Answers

World milk production rose at an approximately constant rate between 2000 and $2012 .^{14}$ See Figure 1.24 (a) Estimate the vertical intercept and interpret it in terms of milk production. (b) Estimate the slope and interpret it in terms of milk production. (c) Give an approximate formula for milk production, $M,$ as a function of $t$ 23. (FIGURE CAN'T COPY)

How you're looking at? Uh huh. Not production. So let's see, we're only about 50 years here, but we're gonna go. Number of 30 firms, number firearms in thousands versus the not bruised millions of pounds. All right, so if we described a couple of these points here, Looks like when they were 2010, there were 63. We were getting pretty organs. That's 100. This is about 200. Um, there's about 100 groups that 1000 100. 200,000 hurt. Yeah, 300,000 home. All right. So number 330 1000 people preaching part. You need to go out right there. Um, 69 1 for three. Okay. 1 93 1. 48 um, 1 40 times in 1 55 567 from the age 1 77 and 63. 1 93. Next. We've got, like, a slight exponential decay. It looks like so I did not try that very well. Hopefully you can tell that supposed to be, um all right, so we're gonna let's go toe longer. Ethnic model for this, Um, if you use he, uh, graphing calculator, there's lots of ways. Thio do this by working by lots of different ways to do this. And it all depends highly on what you used, but it will end up being about 330 went through five minus 34 point five. It's natural light of X where X is the number of firms. And why is the all right is the amount of knocking joins of parents? Yeah, what kind of a graphing utility you are using? All right, So if you graph, that's gonna actually look quite someone to the screen girlfriend here. And in 2008, there were 67,000 dairy farms in the United States. If we played, uh, 67 into this equation right here for X and you will get that it they produced about the plane, Um, 67 tracks right there Don't get about, um, really close to 1 85 billion tons. I've knock. So since the actual no democracy 100 you build problems, the estimate is, um is about five billion homes less? Yeah,

In problem 71. The information is given that we can interpret the point on the graph 0 124 to be the number of farms in 1997. So in this case, are variable X is the number of years after 1997 and are variable. Why is the number of farms? So when we look at part A and we, we we begin to start writing an equation. We know that our be value is 124 leaving us on Lee to find the n value or the slope. In order to write or linear equation, we can use the 0.0, 124 and 1 117 to assault for the slope. Why? To 117 minus y 1 124 over acts 21 minus zero leaves us with a quantity of negative 7/1. So our slope is negative. Seven. Now we can write the linear equation Negative seven ax plus 124 equals. Why? So here we are, with our linear model for this equation Next in part B, we want to explain the meaning of the slope. Well, the slope in this case we have identified as the Value negative seven. In this case, we're talking about the number of funds so we can interpret the slope to be number of farms we eliminated each year. Bastar 1997. In other words, there are seven less farms Fiji approximately because this is just a model, so that's important to keep in mind. Finally, in part C, we want Teoh. Figure out the number of farms in 2004. Well, 2004 is seven years after 1997. So we're looking at an X value of seven. We can substitute this value into our equation. Negative seven times seven plus 124 equals Why, which will give us the number of farms in the year 2004 Negative 49 plus 124 will equal why and thus there should be approximately 75 farms in the year 2004. So we have our solution 75 farms and there you have a B and C of problem number 71

So this is the given question. This is the graph in it is that they're equation in part it is given We have toe shifter Grafton units to the left. So the front or the transformation which we have to uses govt is equal to FFT into 10 place are deep question. So let us a few t placed in in the other equation on get the expansion for us. So Jean, off he is GOP is equal to 0.5 in too deep lest any hold square minus zero point to the seven into people s turn Bless 25.7 letters Expand this deep Listen, old square The formalised is quick Presby school place to way be so letters writer down It is 0.5 in o t Square Bless 100 plus 20 Then it does minus zero point the 70 minus to the 0.7 bless 25.7 So after visit liver even get the equation as so This is the question which we will get We cannot write this in the standard form because this does not have any life terms Now we have to plot gov t and f off T in the graphing calculator tells you that. So this is like that. I think calculator don't know that doesn't enter the functions for us. We are going to put f off B So if he is 0.5 p square, that is extra square minus zero point to the seven. The so that is X. We're taking Dia's exterior less 25.7 point in seven. The next question is 0.5 x square minus is he don't 0.7 bless 22.5. So these other two we questions before she question is a 52nd equation as lofty. No, let us change. The windows are things as we have observed a graph in the but Dad long before so xle it'd be from as the the autograph shift lower 10 units or to the left. So let it be, uh, like minus 12 and maximum is 20. Letter B 22 B under each unit is stool on. Why you many mama's 16 on why you maximise for years on each you noticed Go again. So now let us see the graph. So the blue languages farming. Is that half of 50 under the headline is the graph off GOP? Now we have two. Very fine over there. This govt shifter fire 10 units to the left off this graph that is this is correct on on the transformation. So first, let this tree is the point on the y axis. That does because roughly 25.7. So let us take one. My equation. US 25.7. Now let us see letters photograph. Now the black line is the line off is equal to 25.7. Now let us see the intersection Point. We are ready for the blue line that is here, the blue liner black line. And this excites roughly 25.7. So let us take the deadline on the black line. So it is just excited. Minus 10. That is it. Shift in units. I don't wait 25.7 for the safety letters are doing for the blue line Also. So So you Just a minute. The blue line on Duh. Oh, Luckily it is 25 points, so we have very fired graphical

In order to find your why intercept You would want to plug in zero for X. If he plugged in zero for X, that means we would have. Why equals negative 0.59 times zero plus 40.53 Well, zero times anything is zero. So certainly negative 00.59 is anything. And so that does go to zero, which means we'd be left with Why equals 40.53 which would be our y intercept? Or do you? Technically, the Y intercept specifically would be zero comma 40.53 Now, the real catch with this question is, when it asked you what it actually means within the context of this problem, this is an interesting one. Because if you look if you read the question, it says that what this function is supposed to be modeling is the per capita consumption of whole milk in the U. S. Since 1945 made from 1945 and after. So when we're plugging in, zero for X, Yes, X does represent the number of years but specifically represents the number of years after 1945 meaning this isn't like year zero or something like that. We were talking like Are we B. C A. D? Things like that were saying 1945 is the beginning year. So our Y intercept represents that in 1945 40.53 gallons of whole milk were consumed per person. You probably you want to be specific that we're talking about in 1945? I mean, you can see the 40.53 and I know you guys can get that part. It's important that you understand that we're not talking about in year zero we're talking about in year 1945. Okay, after that next part of this problem asked you what the slope is. Well, our slope, as always, is whatever comes in front of X. The coefficient of X, which in this case would be negative zero 0.59 if you want to represent the slope is a fraction that it would be negative. 0.5 9/1. One of the two, right. Depends on how you want to do that. Um, again, I would put since 1945 in your explanation for what is the slope? The same way we did for What is the Y intercept mean when it asked, What is the slope? Me and I would also say since 1945. But then, besides that, obviously the number is actually negative. 19450.59 What you could say, though, if we want to put this in real life terms, people don't usually say negative 0.59 you would say, Ah, something like 0.59 fewer gallons of whole milk each year, you could say could say Americans, since it did say, for the U. S. Have consumed 0.59 fewer gallons of whole milk per year. Or you could say each year if you wanted to. That's how I would say that does not mean that's the way you have to say it right? Obviously, 0.59 is the important thing, but you could have just said they confuse. They consume negative 0.59 gallons of whole milk each year, But that just doesn't sound as good as saying that they're consuming fewer gallons each year. That's how you'd say it, uh, you know, realistically. But either one of those would still be technically correct because it is negative. 0.59 That is still correct. OK, all right. Onto the last part of this, then where asked us to use the graph to estimate the per capita consumption of whole milk in the year 2000 and then use the equation to determine this number. So, assed faras estimation, you'd want to go look at the chart, right? You wanna go look at the graph that they give you remember, zero represents 1945 and then we're talking about three years after that. So whenever it's asking about the year 2000 the important question for you to figure out is how many years after 1945 is 2000 anyways, while easy way to figure that out. If we have the year 2000 and we want to figure out how far away that is than from 1945 that's a subtraction problem. We want to know the difference between those, right? So if you just take 2000 minus 1945 you will see that they have a difference of 55 years. Okay, so that is what our X is actually going to represent here, because again, remember, x represents the number of years after 1945. So in this case, if we're talking about the year 2000 that's 55 years after 1945. So in order to estimate you'd want to go look at the chart, find 55 on that X axis and see what you think the Y coordinate is at that spot. I mean, you know, it's estimating that's kind of on you guys to do. However, you know, that's That's an opinionated question because different people might estimate a little bit differently. The guaranteed part that we can do is actually use the equation to determine what the true answers. So our original equation waas. Why equals negative 0.59 x plus 40.53? We can figure out all of us together who can figure out exactly what it should be because we know the 2000 is 55 years after 1945 which means all when you to do then is plug 55 in for X. So if we do that, we would have. Why equals negative 0.59 times 55 and then plus 40.53 order of operations says that we would start with the multiplication rewrite, the why we've got negative 0.590 point 59 that we want to multiply 2 55 That would give you negative 32.45 Now we need to add that to 40.53 If you take negative 32.45 and add that to 40.53 looks like you would get why is equal to 8.8 And remember, we do want to go ahead and label this things. This is a real life for a world question. So what is y supposed to represent? Why is supposed to represent the number of gallons of milk? So we want to say 8.8 Galan's. That would be a good final answer.


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