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7) fThe spread of a virus is modeled by V(t) = -t? +7t -4 where V(t) is the number of people in hundreds with the virus and t is the number of weeks since the first...

Question

7) fThe spread of a virus is modeled by V(t) = -t? +7t -4 where V(t) is the number of people in hundreds with the virus and t is the number of weeks since the first case. Find each and be sure to explain if it increases or decreases and by how many people: a) The Average rate of change from 3 to 5 weeks and interpret the answer.b) The Instantaneous rate of change after 2 weeks and interpret the answer

7) fThe spread of a virus is modeled by V(t) = -t? +7t -4 where V(t) is the number of people in hundreds with the virus and t is the number of weeks since the first case. Find each and be sure to explain if it increases or decreases and by how many people: a) The Average rate of change from 3 to 5 weeks and interpret the answer. b) The Instantaneous rate of change after 2 weeks and interpret the answer



Answers

Flu Epidemic Epidemiologists in College Station, Texas, estimate that $t$ days after the flu begins to spread in town, the percent of the population infected by the flu is approximated by
$$p(t)=t^{2}+t$$
for $0 \leq t \leq 5$.
a. Find the average rate of change of $p$ with respect to $t$ over the interval from 1 to 4 days.
b. Find and interpret the instantaneous rate of change of $p$ with respect to $t$ at $t=3$ .

Okay, so we want to find our rate of change of the population infected at time. Cheese equal to 32 Here. We're gonna take the derivative at time. Three. So this is deep within our limits as t approaches three t squared plus two t. I know we need p of three that you go through three squared, plus two times three, which is six. So that's equal to 15. So that's minus 15 over T minus three. So in our noon Rita, we contracted us into a T plus five times T minus three. Looking counsel outs are like terms and how Using jacks up, we get three plus five, which is equal to eight.

So we're given, um, the rate of change or the weight of infection off Children here. But this formula we're gonna graph here on the first thing we have to dio is we have to make a sick in line. I mean, days, four, comma, six. So that's gonna be this is four. That's a six. Right? So let's just make the line here. Yes, right on. We can see that at six. It's hovering around 20. It's hovering around 7.5 on. Then the second line out, it's fell to 14. This is 12. This is 14. That's going to be the seeking heIp right on. We have to calculate, uh, the rate of change right in person so you can just do is we can calculate the difference on you can just divide right. So here it's 4 to 6, though the Delta X here would be to on Delta and T hotels, and here would be seven to sure it's gonna be around 7 to 20 e guess so, around 10%. So the answer would be around 10% for for 2014, we can see that the rate somewhere around 10 to 7.5. So it's gonna be 2.5 by two, which is gonna be 1.25%. So that's part of my part. B. We're being asked, what is the rate of decline Greater AT T 0 to 8 or physical 16? So we can see that physical to eight, the decline to slope years greater than physical to see where it's slowing down. So we can say that AT T is equal to eight. Decline is greater. That's in part C. We're being asked to calculate the rate of change so they can just differentiate best, which I've already down. And then we can put in the value of and it's good to 12, which is coming out to be around 0.98%. That's

So we're having a spread of a virus model by the given function uh And equals, we could just call it a bex are function equals negative X. Cute plus 12 X. Word where X. Is going to be the time And then that's going to be from zero 12. This is the graph that we have here and we'll make X little bit shorter. Sit on the negative three. This is the graph to wind up having. And we see and is the number of people infected in hundreds. So we want to know the maximum number of people projected To be infected and that's going to be 25600s of 25,600. And then we want to know when the virus is spreading most rapidly. So if we look at the crime of X, we see it spreads most rapidly at T equals for which would be four weeks.

So to do this question, we are given an equation and report support A. And if we want to find the beginning of the the susceptible people at the beginning of the pandemic, the beginning represents T equals zero. So we can just plug in t as zero for in this equations will do f of zero equals 15 1000. You mean negative 0.5 times, times zero. And this will just be people. You could have also quickly just realized that the initial is just gonna be this value. So you could have done that trick as well. But I just solved it out for making it clear as the why Now for B, we want to know when 10 days have passed and now T is equal to 10. So f of 10 is equal to 15 000 e negative 0.5 times 10 equals. I'm going to erase people here because we know that is, and I do not right with enough room. But whatever zero okay, proposed that into attack later and we can get five attempts. 10. We'll get nine zero 98 about I'm running, but This is our amount of people roughly and then last but not least, it says after three weeks again since T represents days and now we're given weeks. We're going to do three times seven to find in number of days, which is 21. So Teague was 21 so f of 21 is equal to e negative. 0.5 times 21. And then we get 52 49 people and I rounded off a little bit. But this is this is the answer. So let's make this clear. That's a four 5 to 49 And again, these are all in people is right, people, people. So these are all in people and right here these are our three answers for part A, B and C.


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