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.