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The populalion density irelliesLeld given by pIX y) = 1C0 where O<x < 60 and O<y< 10, andyIzel, andIne number TirelliesDelermine Ihe total population Ti...

Question

The populalion density irelliesLeld given by pIX y) = 1C0 where O<x < 60 and O<y< 10, andyIzel, andIne number TirelliesDelermine Ihe total population TirelliesfieldThe tolal populalion ol fireflies(Simplily Your answer )squato

The populalion density irellies Leld given by pIX y) = 1C0 where O<x < 60 and O<y< 10, andy Izel, and Ine number Tirellies Delermine Ihe total population Tirellies field The tolal populalion ol fireflies (Simplily Your answer ) squato



Answers

The population density of fireflies in a field is given by $p(x, y)=\frac{1}{100} x^{2} y,$ where $0 \leq x \leq 30$ and $0 \leq y \leq 20, x$ and $y$ are in feet, and $p$ is the number of fireflies per square foot. Determine the total population of fireflies in this field.

And that's a question that say that thesis states are Groups are grouped into 10 in groups on into 10 regions on the two largest groupings or regions are the Heartland on the southeast, as shown in the tables. So these are the states in each region, on in each estates it It's mentioned the population in interstate on the total area off each state in both regions. So in first part, eh, it asks for the total population off each raised lesion. So the daughter population is just the summation off the whole population off each state. So just ad thesis numbers here, Andi, you'll find how much of the total population off each region as shown here. This is the total population. Just at these numbers on, the answer is given Here. So what is it? The answer off port, eh? So arrived here that this is answer part, eh? These are deep total population off these two regions. Now, in part B, it asked to find the total area off each region on the total area is again the summation off the area's off the states. So at these numbers off off the region, Heartland on at the area's off the region's off the states in the region southeast as shown here, this is the total area off the Heartland on the total area off this house is so this is you are to be now in part c it acts. What's the population density in persons? Bear square meter off off square mind off each region which means is too That's to divide this number depopulation bear area as it asks for the density population pair area So people were Meyer squared Andi, just divide the total population that I found in part A over the area found in part B And this gives ditto the population density as people in persons bear square mind. So this is deep population density 37.15 and for the Heartland region and for the 1000 East region just divide the same in the same procedure The population over the area on this gives depression This tea in purses Fair square mile on. This is 1 22.11 Andi, this is the answer off part see now in part D at us to confuse the population density off each state. So I have to find the population density off each state individually. So take for jumping in the state, Loa and the profession does. It would be the its own population over it's only area. So this one off this number over this number at gifts approximately 52 on the same applies for the rest off states. The same applies for the rest of states on. Then we have to take the average off the seven states population densities for each region, which means toe add thes population densities that you found for each state, add them and then divide by the number of states. So just take the average. In other words, it's taking the average off. This population densities off thes states, since the number is seven. Just add these numbers and divide by seven. So divide these. Add this numbers add them on divide. Been divided by seven. The answer would be 37.75 for the region Heartland and for the Southeast, it's the same procedure. But after product, the population this off each state at the population densities on divide them by the number off the states, which is seven on this gives 118.6. They are slightly close to the previous procedure used in part, See, and this is the solution of this question. And as these numbers are the solution off Part D.

In this problem of logarithmic function, we have given that and Irwin population density model is a formula that relates the population density D. So this is the population density D 1000 miles per square. So this is you in 1000 per mile square to the distance X. In miles. So this is your exit miles from the center of the city. And formula is given wide is equals to A. To the power minus B. X. For for central density. A. And the coefficient of dickey is B. So this is here is the central density and B is the coefficient of decay. So this is the coefficient of decay. Mhm has been found to be approximately for many large US cities for the city of Atlanta in 1970. So this is the data for Atlanta in 19 seventies. That is A is equal to 5.5 and B is equals 2.10 At approximately what distance was the population density? 2000 per square miles. So we have given that the density is equal to 2000. Well it's square miles. So this is here 2000 but it's square mile. So for this year the school to 2000. But in this data is 1000 per mile square. So that's what we hear. These equals to two and A. Is equal to 5.5. And this will be E. To the power bi equals 2.10 And this would be ex and the X will be in mile. And now we have to solve it. So when we solve it this would be like this E. To the power minus 0.10 X. Is equal to two divided with 5.5. And now that means here this will take the island. So this would be minus 0.10 Exit equals to Ellen two divided with 5.5. And now we have to solve it. That it's Ellen two divided with 5.5 is equal to this what we hear minus this is minus 1.116 This is the value of Ellen too divided with 5.5. This is minus 1.0 point 1.0 116 So this is minus 0.10 X is equal to this value. That means X is equal to now. This can be cancel out and this will be 1.0 116 divided with 0.10 That means when we solve it, the C. D equals two 10.116 miles. So that means this is a distance that egg 10.116 miles. The population density was 2000 person but Miley square

Yeah. So number 71 in section 4.4 is a problem about urban population density. How many people there are per square mile in um an urban setting? And we can see that they're giving us the formula that represents the density to a constant A times E to the negative B X power X is the number of miles um for the population that we're looking at and B is also a constant. So in the city of Atlanta in 1970, They did a study and found the constant a was equal to 5.5 And be was equal to uh .10. So that could be like a rate that it's decreasing or increasing in this one. We're assuming that the population is decreasing since that B is negative. And the question is posed that if the density is 2000 people per square mile, what is the number of miles in distance that we're looking at? Right? How how many miles maybe from the city center? We're looking at this density. So we're going to try to solve for X. Here algebraic lee. So we have to be careful right, because the density is in thousands per mile. So I don't want to enter the left side as 2000. I want to enter as to that would be 2000 people per square mile is equal to Subsequuting the 5.5 in for a. And then the .10 in for b. And remember there's a negative sign there, we're going to solve for X, which is the number of miles. So when we solve an exponential function, the first thing we want to do is isolate the base with the exponent. Sure. And then I'm just gonna leave this right now as this decimal solve it kind of in an exact form here and then I have E. To this power and my variable X is up in my exponents. And any time we've got an exponential where are variable is up in the exponents. We're gonna do this, we're gonna change the form, we're going to change it to its other form which is a log arrhythmic form. So since my bases e. Remember log base E. Is natural log And that number two divided by 5, 5 is what goes inside and a log rhythm equation is always equal to the exponents. So I will have to do to solve them four. The number of miles is divided by the negative .10 on both sides. So if we do that we get the X is approximately 10.1 mi. That's the distance that we would be measuring the population density 10.1 miles.

So did you. Their aggression number 2 87 in accepts is Indicates the year and hear why X isn't against the population. Maybe so for the year 1990. Depopulation, ese. Your duty extended. So here, 1990 Year 5600 seven borders 1995 in depopulation. Finding fries you. So you're 1995 hear why? 950 This is our second board and so on. So as we've been seeing here, trained appears Sr. Okay. No. Our question is that if we wanted to know when the opposition will reach 15,000 we're dancing dancer involved, interpretation or extradition. So the answer is extradition. Because of your 15,000 He's outside the range of the data here. Ranges 56 double zero under the maximum. Really? That is 69 double zero. Okay, so here are 15,000 does not lie in the range, so it would be extrapolation. Okay. Thank you.


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