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(10 pts) community had population of 2500 when built = new city hall; Eight years alter the new city hall was built, the population of the community Wis 4250. Assum...

Question

(10 pts) community had population of 2500 when built = new city hall; Eight years alter the new city hall was built, the population of the community Wis 4250. Assuming the same rale of exponential growth; what will be the population of the community (wenty years alter the new city hall was built?

(10 pts) community had population of 2500 when built = new city hall; Eight years alter the new city hall was built, the population of the community Wis 4250. Assuming the same rale of exponential growth; what will be the population of the community (wenty years alter the new city hall was built?



Answers

City population A city currently has $36,000$ residents and is adding new residents steadily at the rate of 1600 per year. If the proportion of residents that remain after $t$ years is given by $S(t)=1 /(t+1),$ what is the population of the city seven years from now?

So first what we're gonna do is determine K. So this is going to be um from 164 1000. We end up getting to 235,000. Mhm. That's an equal to 1 64 1000. Eat the Katie. But we know that the T. Value, it's going to be 12. So solving yes, we end up getting our um this is gonna be okay, we end up being R. K. Value and then we can have that Y. Equals uh um why? It goes A. E. To the K. P. But we already know our K. Value and now we're trying to find the A. Value. So all we have to do is plug in when T. Is equal to zero, when T is equal to zero, this whole term goes to one. So we would just get that Y. Equals A. And that will give us our final answer, which in this case is going to be 126,829. right. This right here is going to be the final answer for the given problem, and the units for this is going to be um, it's been referring to the population size, but the final answer.

I just wish you the population before five year was given has $49 okay, and our each of the publishing increases. This is his 1st $40 million. If you call that as a the publishes a shapeless and the each year the increasing population is five babies. Levy imposed a close to re insults off. So we have the final population off 10 years. Okay, selectors unit this and so population. Oh, good. Five years we'll be as this is a perfect prohibition to the someone over sold out on eternal pretty coalition video player to retain so or left arm. It's tanto blacks For the first time, it's putting in Toki that it's 14 including color differences. A pretty day we can I know that a plus and minus one, you know the okay as required. Essentially, the population at the end of five years of Corporal are really off and we'll be yet okay, lets producer use industry before being told I was 11 minus one into the that is facing because I did Thomas for being my intelligent, less 10 in the fighter priorities. Let me if I tell it to issue decency before 1008 and it Okay, so this movie, the population off five here. So this is an intern solution for this Bush?

All right. So for this one, Number seven, we're talking about population growth. And what is asking for, uh, Teoh come up with a formula for the population of for the girls of the population in the city within a certain timeframe. So this is the general formula for population growth, which is, and of tea, final amount, Ingles and subscript Oh, in this hole, he's constant. Okay, is growth rate and t is time. All right, so for B, it's a two step problem. So they give us the initial amount. The initial mount is 10,000. Okay, Now it says after 18 months, it's going to hit 20,000. So 18 months equals 20,000. Well, it isn't 20,000. Exactly. They're saying that the population will double in 18 months. 10 times two is 20,000. All right, so we have that we don't have is the rate we don't have K. I am. We need cane or to figure out the rest of the problem because then what it's asking for is they're saying, How big will the population get after two years now? Two years? There's 12 months in a year, right? So 12 times two equals 24 months. So 24 months. So how big will the population get in 24 months Now? We can't solve this until we get the rate. So that's sulfur. The rate. So 20,000 equals 10,000? Yeah, to the K. And then T is 18 months. All right, so let's get another color. Divide the 10,000 now. You should get to equals e. Okay. 18 Ah, Ln two. Which cancels out the e que 18. So why not the 18? And you should get k equals roughly around, um 0.385 Now, if you plug Kate, this the rounded form into the equation, um, you're going You're not going to get what it says in the book. So here, I'll show you both ways. We just school up school too much, OK? No, that's not what I know. It's not what I want, Okay? They really All right, So that's plug it in since we have the rate. So we're trying to find on this key, and we start off a 10,000 E to the 0385 times 24 months. Now. When you put that in the calculator, you should get around 25,000 193. That's how much will be after 24 months about now. If you if you saw for K and you put the exact amount, which is K equals 0.385 081 and it keeps going going. So we just, you know, copy and paste that into your calculator and put it here. Then you'll get what the book says, which is 25,000 198 and that's it for this problem.

It's there. So when you right here. So we're gonna use the pft equation to get 10,000 all over one plus 10,000 minus 1000 over 1000 times eats and negative Katie. Then we just simplify to get 10,000 all over one plus nine e negative, Katie. Then we just made this equal 2 2500 when it's p of one. So we know that this is gonna be equal to one two. You get 2500 times one plus nine e to the negative K this equal to 10,000 and we get nine e to the negative. K is equal to three and we get e to the negative. K is equal to 1/3. We take the Ellen of both sides, then we get negative. Cake is equal to out on of 1/3 when we plug in p A four. Since this asking for three years out for the first year, we get 10,000 over one plus nine e toe l n of 1/3 terms for and we got 9000


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