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The population of shortfin mako sharks in a fixed region of the coast of Africa is studied. When obervation begins, there are 460 sharks in the region: The populati...

Question

The population of shortfin mako sharks in a fixed region of the coast of Africa is studied. When obervation begins, there are 460 sharks in the region: The population continues to grow exponentially, and 3 years later there are 600 sharks in this areaa.) Find the growth constant k and round this value to 6 decimal places_b.) Find the rate at which the population is increasing 5 years later: (Remember: Rate Derivative):Round your answer to the nearest integer (whole number) value_sharks peryearGu

The population of shortfin mako sharks in a fixed region of the coast of Africa is studied. When obervation begins, there are 460 sharks in the region: The population continues to grow exponentially, and 3 years later there are 600 sharks in this area a.) Find the growth constant k and round this value to 6 decimal places_ b.) Find the rate at which the population is increasing 5 years later: (Remember: Rate Derivative): Round your answer to the nearest integer (whole number) value_ sharks per year Guidelines for submitting numerical answers: 1. Only use numerical characters. i.e. Enter the number without any units; commas; spaces or other characters:



Answers

Find a formula for the number of zebra mussels in a bay as a function of the number of years since 2010 , given that there were 2700 at the start of 2010 and 3186 at the start of 2011 (a) Assume that the number of zebra mussels is growing linearly. Give units for the slope of the line and interpret it in terms of zebra mussels. (b) Assume that the number of zebra mussels is growing exponentially. What is the annual percent growth rate of the zebra mussel population?

Now thirty four. Under certain conditions, a population may exhibit a poly Lamia growth rate function. A population ofthe blue wells is growing according to dysfunction. Or go about this different function. Hair wise of publishing sergeants and tease. Measured in years. Use Oilers matter weeds. And she does want a pro. Cremate the population in four years. You initial populations. Fifteen thousand. OK, so that's just two oil. Is Mathur here? H He was wanted this case. Initial audio. You need your populations. Fifteen dollars. Okay. T t here is different. We got if you want. They're playing there too. One of where there are three. A lot of cube. Okay, What happened? Okay. Anyway, we don't actually cares in park because it's one fifteen problem. And this guy is Ah, it's going to be I like it here. Line eyes be five, three, five. Cross your point there. Sue would apply Claire Cave far Claire three, if by far. Phew. That's a huge number that near wise be five plus c five much cry one. This is not correct. We want to lose the fourth year. What happened here? Back to your wife. Elective. Why? Plus their point there till why Square Place serpent tears their story. Oh, my God. Hear their story. Terror. There are three. What happened here? You have to be locked, sir. Okay. We've got the lumbering the Force year. So is wants us. Huge. Doesn't look so good and true. Is that to point the story to the ten? What about Kendall? The two. Thirty seven. That being really so? Okay, let's check it. Fifteen yards. Oh, why is population two thousand the wise fifteen? Actually, activity employees terrible. There to fifteen square plus two point. There are three. Fifteen. Cube eat. Okay, correct. So yeah. So m point zero one seven. You know, there's some important zero one seven for seven o once. Shit approximately. Okay, thirty four.

The solution to the question number 108 His here we are, given that affects is equals 2608 four into E. To the power 0.1 to zero X. So where X is a number for three years since 2000 So now for the part when X is 10 years from 2000 to 2000 and 10, we have effects is close to 6084 E. To the power 0.1 to zero in two weeks. So putting 10 in place of X. You will get effects. His calls to 6860 Yeah. So the approximate number of population given by the exponential function is six 860 million. While the actual population was 6853 Yeah, million in here. 2010. The estimated population is seven million greater than the actual population. Now, moving towards part B. When access 20 years, that is from 2000 to 2020 14. 20 in place of X. You will get your Yeah, 20 years 7734 And when X becomes 30 so half of the party will be 4 to 87 to zero. So by 2020 the estimated number of population is 7734 million. Right, Bye 2030. It is estimated to be 8720 million. Thank you.

In 2000 and eight were stalking 5500 droughts. And it has given that every year we're going to add 500 more. Let's talk about any general year a. M. It has given that the population is going to fall by 25% off what it was last year. Hence, we have 0.75 times a and minus one and plus we're adding fiber and more. So this is our records of sequence. For 2009 the question is going to become 0.75 multiplied by 5500 That's 500 which will give me 4625 2019. 82 as 2008 was a one. 2010 will be a three where we follow the similar pattern and we get 3969 and a four will be, that is the value for 2011 is going to be 3479 So we have 2000 and 89 4010 and 2011. Now what is the graph going to look like? The graph off the DK is going to look something like this which means that the population is going toe DK at a decreasing rate and after infinitely long time there will be. We find that the number of trouts are going to reach an equilibrium at around 2000 because they will be decreasing or the decade is going to keep on decreasing. Hence, this is my answer.

In this fish hatchery situation. We want to find the harvesting rate as a function of the amount of fish be. And so we could start in part one part A with converting this differential equation to an initial valued solution, which is equivalent of what we're tryingto find here. And this is going toe. Give us Remember if we had a When, When we have a linear differential equation, then we're gonna have an exponential, original equation. So this will be a C to the e negative. Katie, we know we have a negative K values 0.1 or 1% and then times t minus B over K. And here we're going to leave it in terms of B. That's one being minus are negative b over, uh, Meg. Over. Sorry. Zero point cereal one. Okay. So to simplify this or cleaned it up a bit, I'm one thing we want to do. It actually sold Percy. So we're gonna use the initial value on the right side, which tells us that population in the beginning of the problem at time zero it's 500 fish. And so then we're going to have that. This is people too se times e to be zero, and that's going to be one. And then we still have this be term. But we could go ahead and call it plus cause minus minus B over 0.1 Or we could flip that because that's the same thing as 1 100 So we could really call it 100. Be should be the same thing. Is that there? Um and that will then allow us to come up with a term for C. So let's roll down just a little bit here, So really, that constant c is 500 minus be over 21. Sorry, this is a plus. Yeah. And, um, since that's the constant C and let's just go ahead and on this writing the whole thing. Why of tea? The number of fish as a function of time of years that's finding equal. Um, 500. This is all a constant. So let's put it in parentheses. Sighs to the negative 0.1 t and then again, plus over 0.1 Okay, so that's for port A for part B. We're basically probably fed all these on the same screen. Now we're going to replace, be with 40. So that's going to be that, uh, 40 fish are harvested per year. This for a year, okay? And so we could replace the B values there. And in which case, when we graft this, it's still going to have an initial height. Oh, well, we're told that we initially have 500 fish, and so that's what we should expect here. And in fact, when you plug in 40 here, um, you'll end up realizing that this graph will in fact tell us this. And then it's going Teoh slope off. And so, if you were to describe this graph basically ah, slow change and fish followed by a more gradual, more gradual steepness and, uh, rate of decrease. And so towards the last, you know, year two of these of this fish hatchery, it's really dramatically dropping off, but slowly at first. And so, um, that's well, completely reduce the population 20 after about 13.4 years. That's an example here. This is just helpful for the next problem. For part C. And I've included Part B and part. See, I've written them out. It's a little too complex to write them out again here. So I have those written in the answer keys for this and then when, um, be the number officious 60 per year. Well, before you we answer it. Have you expect the population to change? Is it going to drop off faster? Slower? Um, if you said that it was faster, that's right, because the, uh, b is kind of the rate of decrease. And so we were to redraw this and again. This is why of t said a fish hatchery population. But it's gonna be relatively the same graph, right? It's still going to start with the same population of 500 and going to drop off, um, in 8.7 years as, ah, um, relative comparison between


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