Q2: The following table shows the distribution of the Iraqi and non-Iraqi workforce; by sectors, according to for the labor force inventory for the year 1980. Secto...

The following table gives world oil consumption, in billions of barrels per year. $^{1}$ Estimate total oil consumption during this 25 -year period. $$\begin{array}{c|c|c|c|c|c|c} \hline \text { Year } & 1985 & 1990 & 1995 & 2000 & 2005 & 2010 \\\hline \text { Oil (bn barrels/yr) } & 20.9 & 23.3 & 25.6 & 28.0 & 30.7 & 31.7 \\\hline\end{array}$$

Okay, We're gonna create a bar graph using a some census data. We're gonna start with our population. Population is going to be our Why Access. Ah, big pet peeve of mine is Make sure you lay able label. Your access is so we're gonna put the population of the side. Of course, the bottom Rudy see always starts at zero, and then our numbers air so large, we are going to put 10 million on our first line. Remember, the line itself equals that number. Okay, the line itself. 20 1,000,000 and then we're going to 30. And you want to label up your ah bars as far as you have population, Um, you might want to go one increment higher, then the amount you have this range will always very based on your data set. So you gotta make sure you range is completely personalized to the data set that you are working with. Okay, so I went up to 70 million and population, and then our other piece of data is going to be h age within this populations. So nice and neat. Make sure you have labels on your paper. Make sure you're spacing nicely. So we haven't. Age of 0 to 14. 0 14 is 60 million. 2 to 4. 094 So is it a little bit over 60 million? OK, and then we're going to make that bar, okay? And, Phil, it'd please, please, please use a straight edge and color very nicely on your paper. Uh, technology isn't as forgiving for me. Um, and that was 0 to 14 and age. Okay. I hope yours looks so much better than mine. Um, then we had 15 to 34. My skip one do 15 to 34. 15 to 34 was 79 million. Oh, I should have definitely went up a whole Another data point over here, so I'm just gonna go ahead and extend it. So 15 to 34. 79. That is so close to eight. I'm going to get it right up there against that 80 million. Make that bar. Okay. Make that bar come all the way down. Color it in. Okay. Make sure labels my coloring. Looks like I'm a second grader, but we have the information in their 35 to 54 35 to 54. And that's gonna be 82. So we want that one just above that 80. And we're going create that bar in that bar grass. There we go. OK, and then we have 55 to 74. 50 5 to 70 4 55 to 74 is 42 million for 94 5 71 So 42 million. Just over 40 which is right here. We get a good little bar going, okay? And then finally, we have 75 plus and age 75 older, which iss 16 0 that one's right down in this range right here. Just over halfway between 10 and 20. So we just have a small bar for that one. Okay, so we have, like,

This question asked us to find the average rate of change between 1940 and 2000. You know, the average rate of change is given by this formula delta L over Delta T, which means we can subtract our values for l has given in the table, then divide by our years. We know we're looking from 1950 to 2001 therefore were subtracting on the denominator. When we do the calculation, we get 1.608 and this is in terms of millions off metric tons and then it's per year. So this is the

So from the data, we can see that a is equals to zero point 4017 and B is equal to 46.3556 So therefore, why is equals to because, you know 0.4017 eggs plus 46 point 3556 So this wasa party not in subpart B, our equation would be wise. He calls too 0.4017 x minus. 1970 1970 Blessed 46.3556 So using this equation, we will find are by So why is equals to 0.4017 for the year 2050 minus 1970 plus 46.3556 So therefore the value off is 64.4.

Hello, everyone. Welcome back to New Parade. So we're on section 3.8 on page 4 to 43. Where our number six about six A. All right, So we're given a table of population, uh, in million's for India for 1951 1961 1971 all the way up to 2001. Part a used the exponential growth model. So it's pft again. Population in millions of people in India off t in years. Uh, is p zero heat of the Katy. Okay, Already. So use that model to predict the population to have one and compared with the actual figure. Alright, So in 2001 they have, ah, population of 1000 29 million people. In other words, almost over a billion people. A little bit over, let's say, p zero, let's see. So let's say P zero is what they give you. 1951 is when we're starting. Right. So 361 million. And then it says to use 1951 1961 soapy of 10 years later is gonna be on the table. We have 439 million already, so I think this is enough information to get Kay. And then we can plug in 50 to get in there. Smith for 2001 because zeros 1951 and 10 is 1961. So 50 will be 2001. And that's that's what they want you to predict. Okay, so I'm going to say that, um p of 10. What's right? So p of 10 is 4. 39. That's gonna be p zero initial population. Let's say we're starting in 1951. Neither the Katie but T is Ted. So it's suffocate. Divide by 3. 69 3 61. And take the log of natural log of both sides. Get rid of the natural Basie. So you got Ln of 4. 39/6. 31. Sorry. 3 61. Uh huh. His Ellen of indicate the 10-K, but that's just 10-K. So Okay, is 1/10 of that. So Okay. Was okay. Is 1/10 the l N of 4. 39 over 63 61 which is approximately 0.19 61 366 zero point. 0196 Very close toe too. right, All right. So now we want to do is find Pier 50 which is arrested for the population of India in 2001. Theatrical data here says 1000 29 million or 1.29 billion. Right. So I'm gonna say that, um here 50 he's gonna be the my P zero times either the Katie it over. Uh, let's write it this way. 0.1 Ln of 4. 39 over 6. 33 61. And then let's plug in times 50. There's only exported here. The all that and that approximates to the nearest million 962 million people, which is an understatement based on the table, which has 1029. Alright, so that's part of it. Mhm or B Used expenditure model of the census figures. Um, sure. Um, from 61 81 to predict the population 2001 and see how much better than it. If that's any better. And use your model to figure out how many people. How about the population is 2010 and 2020 which is extrapolating beyond the table table Substitute 1001. Alright, so it's two party. All right, so, four b. So we've got. And so they want to use 61 81. Okay, so let's say P zero is a population in, um 1961. And that on the table is 439 and then they want you to use p 81 which is 20 years after that. So p 20 so p 0 1961 p 20 is 19. 81. And that population right now is the table 6 83. Mhm. So what? Why don't we say that? Um, Peel? Let's say P of 20 is equal to p zero. Let's make this p zero. Right? Either the Katie but T is 20 to suffocate again. Divide by 4. 39 8 38 6 83 divided by 4. 39. Mm hmm. He goes into the 20 k I'm writing. So we take the natural leg both sides to get the l N of 6. 83 over 4. 39 is 20 k. So they've ever 20 to get. Kay is 1/20 of the l N of 683 over 4. 39 which is approximately 0.22 already. So now if you want approximate, um, the population. Okay, let's see. Oh, in 2001 Which on the table is 1000 29 If 1961 is p 0 2001 is P 40. Right? So let's finish this question. P 48 will be our estimate for the population of 2001 is gonna be 4. 39 looks equals 4 39 times Edoga. All right, so I'm gonna say this 0.0 5/20 the l N of 6. 83 over 4. 39. Okay, time is 40 years. That's all in the export to eat it, all of that. And that comes out to Let's take the nearest million 1058 which is a little bit of overestimate compared to the table, which is 2029 million people. All right, so part part B says toe also estimate p a 2010. I would not be, um, 50 would be 2011. So 49. Okay, So Pier 49 Sapir, 49 do the same thing. You know, this is but you have a 49 instead of 40 Now we get 1290 million people. Is arrest mint for 2010. So this is 2000 and one. There's 2010. No. So in 2020 2020. So it will be p of 59. Right? So 2020 are extrapolation from the extending the data p of 59 right? Yeah, that's approximately. What did I get now? 1607. Which you could google up and see if that's actually publishes his today, if you like, are now Part C. Says, um, graph both of your models The one compartment for part B and see which ones Wait, What does it say? From Partner and, uh, compared to the actual a scatter plot And are these reasonable models? And I grabbed him on May 24 ce from book emulator and they all they both follow the model very closely. Um, on my calculator I got a exponential regression of 1 21 0.682 times 1.2 14 times. Either Let's see science either no times one point 0214 to the X or to the tea right, which is very close to both of these models that we just came up with a figure out from there. Very close. So it's reasonable. They're all They're both reasonable. All right, that's that. That's it for this question. Thanks for watching. I hope that was helpful.