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Tntcrested In the Annual Salaty ot Elcctroniz; Assotuled (ENI) muser s anu wc nnd tfwt lor # smpla ohrainirig eample Incan Wthin = Faen tha population Ineon WHUIE b...

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Tntcrested In the Annual Salaty ot Elcctroniz; Assotuled (ENI) muser s anu wc nnd tfwt lor # smpla ohrainirig eample Incan Wthin = Faen tha population Ineon WHUIE br-Iow).Suco € probabilmAaSmpllng distributionOI" 7J0.0NSIJmst < 52_001MT<S1,HoiS,ou S086iS2.ui1 06 Dutu(b) . Ict tha population mcar De 51,600 Bnd & wanat the probabilil , Frat ^ mithin 43500 tnc ponuiatior incoi[anlnd VoueantMciIount UecImai Mincds )FhmllWuo ucdAivei O (a} fol Ramp 4 972 160

tntcrested In the Annual Salaty ot Elcctroniz; Assotuled (ENI) muser s anu wc nnd tfwt lor # smpla ohrainirig eample Incan Wthin = Faen tha population Ineon WHUIE br-Iow). Suco € probabilm Aa Smpllng distribution OI" 7J0.0 NSIJmst < 52_001 MT<S1,Hoi S,ou S086i S2.ui 1 06 Dutu (b) . Ict tha population mcar De 51,600 Bnd & wanat the probabilil , Frat ^ mithin 43500 tnc ponuiatior incoi [anlnd VoueantMci Iount UecImai Mincds ) Fhmll Wuo ucd Aivei O (a} fol Ramp 4 972 160



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The graph models the population $P$ (in thousands) of Sacramento, California, from 2003 through 2012 where $t$ is the year, with $t=3$ corresponding to 2003 Also shown is the line $y=450 .$ Use the graphs of the model and the horizontal line to write an equation or an inequality that could be solved to answer the question. Then answer the question. (Source: U.S. Census Bureau) (a) In what year did the population of Sacramento reach $450,000 ?$ (b) During what time period was the population of Sacramento less than $450,000 ?$ greater than $450,000 ?$

In discussion. I'm going to use on my graphic calculator in this corner. Does mosque here were given the population as a function under Time T So have the three. D. He goes thio 0.108 the ballot far and then minus the point to 11 the power three. And then plus the point for the power to that's seven or nine. Okay, Just no 1791 So it would judge you're out a little more here because and will be more than 1000. So that's gonna be the craft. Looks like on we are interested in the X between the zero Judah 14 on Lee. So that's me in the there are options of 14. Andi. Then ask me the population Gove looks like here so we can try to blend the value of the y will be I consent from the 1002 100. 2000? Yeah, B to the, uh um 15 will be easier. June 5 at best. And it makes more sense. Maybe in about 2000. Yes, And that could be the discovery represent fund population in the West Virginia. And we see that the the the beginning point here it will be. This response here were given the value equal to no year after 1990. Okay, so we have here equal to the 792,000. Ah, And then after that, we will see that in the puppy. We want to determine which year the publishing was increasing so increasing for those years starting from the 1990 up to the year off, here will be the values. Ah, I'm just a year after five. So around six year on. So we have up to the year 1996. And after the 1996 the population will go down up to the year after. This one will be 11 point, you know, trail. So will be, uh, 2000 and two. It would be, uh, the population going down. And after the tradition, until the publishing were going up like this on now, in the past, the we want to approximate the maximum population between the 1992 the tradition and far So the maximum population in appears to be this point here, and that's gonna be the year on the 5.6 or Israel. The year of the 1996 to 1995 to the 1996 or 1995 Onda maximum population will be enriched. The population of the I didn't. 822,000, Yeah.

So for question A, we'll have the regression equation. 458 791.8 hour one plus 18.771 year to the power off. Minus Obama Straight E So when t approximate approach to the insanity, we'll have the Teagle infinity here, and those one were approximately equals two one. So we are how the function equals to one plus zero. And here the numerator equals to those number. So that is approximately equals. 2458791.8. And for see, we have the population. Oh, 45 450,000 Eco's to our function. Uh huh. Right, So e to the power off minus 0.113 t equals 2.1 So our T here approximately equals to 60 and for the last one will have the p over b t eco's to the function Pay P times minus P and substitute the number Here. We'll have to point for 6 to 6. Um, tend to power off 97 comes P and assess 45879 one minus P

Question 32 gives you that the population, P and thousands is given by the function. P equals 319.2 e to the K T, where T is representing your year where t equals five corresponds to the year 2005. And it also tells you that in 2006 the population ah is 347,000. Um and this function is spanning from the year 2005, 2010. So for part A, they want you to find what is the value of K and then also if the population is increasing or decreasing. So to do so, we can plug in our givens here. First, we know that our population is in thousands. So to plug in our equation p, you have to divide this number by 1000. So he is 347 said that equal to our equation 319 0.2 e to the K and our T in this case is going to be six. From there, you can take Ln of 347 divided by 319.2 equals e to the six k Ah, And then you can also take Ln of e to the six k from there Ln of 347. About I 319.2 equals six K and they're solving for K. You get K equals 0.1 939 Ah, And you know that because K is greater than zero, your population is increasing because this positive K value indicates exponential growth in part B. They want you to use the model. Predict to predict what the population is in 2015 and in 2020. Are these results reasonable and explain your answer. So starting off with 2015, your T value is 15. Paul unit in p of 15 equals 319.2 e to the 0.139 times 15, which comes out to 300 1000 193,000 58 p of 20 for 2020 or t equals 20 3 19.2 e to the 0.39 times 20 equals 421 3 85. Thes answers come out as 393.58 But because they want their answer. And thousands. I converted them to the full number. Um and this answer is reasonable. If your population is gonna always experience exponential growth, however not realistic, most populations experience something more like logistic growth, where there's a curve where they're experiencing increased rate of growth and then it decreases and settles off heart. See, they want to know. According to the model, during what year were the population reached 410,000. So P equals 410,000. It's gonna be 410 because you're dividing by 1000 410 equals three 19.2 e to the 0.139 t or to solve for t here. So take Ln of 410 divided by 319.2 equals Ln of e to the 0.139 t this gets rid of East. You get Ellen of 4 10, divided by 3. 19.2 is equal 2.139 Teeth solving for T. You get 17.986 around that. That's about 18. That corresponds to the year 2018. So that's when your population will reach 410,000. And that's your answer for questions,

For problem. I know when we were asked to construct a box and whisker diagram for the period 1976 to 2000 and five on for the period 2000 and 5 to 2000 and the living so for the period 1976 to 2000 and five, you were only given the courthouse so called tell one or the first quartile was 5 to 8.5. The median or courts also was 1000 and 14 and quotes all pre was 1400 47.5. This box plus has no whiskers because here we weren't given the raw data. So we don't have our minimums and maximums moving on to the second box plots. Here we were given the road. Dates are hence we have whiskeys. Our minimum was 1585. Our maximum was 2000 and two. Anyone I will quote sell one was 1690 are quotes. All too, was 1812.5, and I'll quotes out. Three was 1000 935. Take notes in order for you to calculate the court tells you have to first arrange your data in ascending order. Then calculate your courthouse. You'll find out. Consult. So we have to find an average off tour numbers, which is 1735 on 1890. Getting the average of those numbers will give you court I'll to over 1812.5. Thank you.


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