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The population $(p)$ of a small community on the outskirts of a city grows rapidly over a 20 -year period: As an engineer working for a utility company, you must f...

Question

The population $(p)$ of a small community on the outskirts of a city grows rapidly over a 20 -year period: As an engineer working for a utility company, you must forecast the population 5 years into the future in order to anticipate the demand for power. Employ an exponential model and linear regression to make this prediction.

The population $(p)$ of a small community on the outskirts of a city grows rapidly over a 20 -year period: As an engineer working for a utility company, you must forecast the population 5 years into the future in order to anticipate the demand for power. Employ an exponential model and linear regression to make this prediction.



Answers

Use a graphing calculator with exponential regression capability to model the population of the world with the data from 1950 to 2010 in Table 1 on page 49. Use the model to estimate the population in 1993 and to predict the population in the year 2020.

In this problem, we're going to use a graphing calculator to compute an exponential regression for the data given in the table. So we go to the stat menu and then into edit, and we type our numbers into list one and list, too. And the numbers I typed into list one represent the number of years since the year 1900. So year zero is 1900. Year 10 is 1910 etcetera. So I didn't type the numbers exactly from the table. I subtracted 1900 from each of them. And then the numbers in column two are the populations. So what we want to do with this is find the exponential regression. And it might be interesting also to look at the scatter plot and see if it looks like exponential growth. So we can go into the stat plot menu. We can turn on plot one when we can go to zoom and go to zoom stat number nine and we can see our scatter plot. Okay, so from here, we want to go ahead and find the regression equation. So we go back to stat over to calculate, and then we go down until we find exponential regression is a bit farther down in the list. There we go. Exponential regression. We pressed. Enter, we're using List one and list, too. We do want to store the regression equation in our Y equals menu. So when you get to this point, you press the variables button, go over to why variables choose function and choose why one and then we can calculate. So if we round these numbers, we have approximately y equals 80.8 times, 1.1 to the X power. Okay, so if you press why equals, you will see that that has now been pasted into the y equals and you and we can work with it. So what we want to do is use this equation to estimate the population in 1925 and predict the population in the year 2020 which just so happens to be the year in which I'm talking right now. So what we can do is use the table for that. So I'm going to go into table set and make sure that my independent variable is set to ask, and that will allow me to type in my own X values. Once that is set, I can go into the table, which is second graf and it doesn't matter if you have numbers here. You can delete them if you want, but it's not going to matter. So for the year 1925 we want to type in a 25 x, And that tells us 110.82 is the population of the United States in millions, according to this model from the year 1925. And now let's type in the year 1 20 to represent the year 2020 and we get 367 million for the population in the United States.

This question asks us to use a calculator toe model the population of growth of the world with data. So you put this did into a calculator. You have, like your accent. You're why I'm using a T I 84 plus then we're using exponential regression. They equate. This should pop up and they should give you an A. Therefore, what we knows, the model is 2614.8 Sex Tom's 1.1693 to the power of tea and then 5381 means 53 81 million and then, lastly, 846 Sex means 8466 million.

So 13 is talking about a town with an initial population of 75,000 and that right there should be a time where you pause and say, Okay, initial population. That's the amount I start with. Which means that means that's my why intercept K or when we plug it into our equation, y equals MX plus B. That's Amar y intercept. I've even heard it called the zero Step because many of zero years it's the 75,000 which is also awesome. But that's what the 75,000 is telling me. That's my Y intercept. And then it says that it grows at a constant rate of 2500. So I called at a constant rate of change or crock. Okay, and since it's changing per year, that's going to be my slope. Cake has a rate of change and a slope or the same thing, and that's the M in my equation. Um, now, here there's one other stipulation that they want us to do. We can't just write at y equals MX plus B. They want the population to be peace on this case. Why is gonna be written? His P for population and X is gonna be tea for the time for the number of years. OK, so it's gonna be in the same format, just not with those letters. So when I put it all together, um, we'll go ahead and use pink. So we'll say that P is equal to that slope 2500. Hey! And then we get inside using X. We used t cause it's per year. So that's time. And then we add in that initial value of 75,000 and then that would be my equation. Okay, so just figure out what pieces you have and put it in a linear equation.

Hi. Welcome to question 165 chakra juice. Uh, this question were given scenario and were asked to Hilda model the pits. That scenario, in the question describes us of population off some 200 growing at a constantly not because of the constant rate that means to ask, That's a linear model. So that means I have I have the baseball more Why? Because to, um X plus B, where m is my rate. B is my starting. I'm out. So, um, the question tells us that's a model using the letter Pete s population soapy. His population is a month. Then he is a function of teeth. So tears are independent, variable. And so now I just need to find a rate, then the starting them out. The rate is describing the question That's 2500. And the starting amount is described also in the question that somebody 5000 the number the other number, everything into question off five years doesn't really matter because


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