use-the-following-information-the-us-bureau-of-the-census-predicted-that-the-population-of-florida-w

Question

Use the following information. The U.S. Bureau of the Census predicted that the population of Florida would be about 17.4 million in 2010 and then would increase by about 0.22 million per year until 2025
Choose the linear model that predicts the population $P$ of Florida (in millions) in terms of $t,$ the number of years since 2010 .
A) $P=17.4 t+0.22$
(B) $P=-0.22 t+17.4$
(c) $P=0.22 t+17.4$
(D) $P=-17.4 t+0.22$

Nick Johnson · Accepted Answer

we have the verbal model. Where we have the for the population is equal to the 2010 population, plus the increase per year times number of years since 2000 and 10. So if we have the floater population is equal to its AP million and then the 2010 population was given a 17.4 million increase per year is 0.22 million and that say there&#x27;s t years since 2010? So, um, here they require the outbreak models, which represents this would be option c.

Chengyu Li · Answer

indiscretion be have two functions does given, which is P 2000 Go to see times e Do the power 2000 times K equal to 16 and the other one is P 2004th equal to see temps A to the power 2004 times K A coat to 17.4. Next step. We use function to two divided by function while so we can try to eliminate a C first because we only want one Bora Bora in the function which is the K can cancel out the sea. So now we have a and we can also use the 2004 to minus 2000. So have Teoh function two divided by function. We have made to the powerful K equal to 17.4 divided by 16. So we used a property that we already know we have lying on both sides we can so that we can bring the folk a dog equal to line 17.4 divided by 16. So it food four divided by four both sides So we can left a k on the left The rice I we have We&#x27;ll do it before. Okay, so we put it into the calculator. So we have K approximately it go to their 0.2 zero and I do seven so we can pluck the K back to the function p 2000 This move. Go to 16 so we can have Let&#x27;s make the seat on the right side and the rest left side. So we have change the side. Okay, we&#x27;ll have more room. So we have approximately equal to 9.75 times 10 to the power Negative 18. That&#x27;s the seat. So until here regard que and the sea Let&#x27;s put it back into functional form. So we have PT ICO too. 9.75 times 10 to the power native, 18 times e to the power. Okay, which is still points to 0 97 t don&#x27;t for about a t. That&#x27;s what we want to get. For the question being, we have to question the function form from the previous question. So let&#x27;s detect what the population and for reader 2000 tents. So that&#x27;s just clocking key, which is 2000 tens that would put the whole thing into the calculator. So regard 19.6 95 Mulee so approximately it go to 19.7. Thanks for watching

Nick Johnson · Answer

do we have the expression here? Why squared, plus X over X and friend To evaluate this win acts is equal to negative three. And when? Why is the coach you sex and secret sex? Okay, so what we have here we have. Why squared? So we have, um, six square. So we have six squared plus or plus X. That&#x27;s plus a negative three divided by x, which again is negative thing. Okay, so that&#x27;s where we happy? Well, six square that&#x27;s equal to 36. They have 36 plus a native. Three are same thing is 36 minus three. And then this whole thing is then divided by a negative three. This is equal to off 36 minus three is equal to 33. We have 33 divided by a negative three. Okay? Or 33/3 is 11. But we have one top numerator is positive of the document is negative. Just gonna be equal to negative 11. I saw the expression here evaluates to negative 11

Charles Carter · Answer

problem wants us to ah, choose from multiple choice answers. An equation that predicts the population of Florida are y axis in terms of X. All right, Texas. Um, so we&#x27;re given this line someone of this. So his ex increases? Why increases so we can eliminate answer choices? Be Indy, since they both have negative slopes of our choices left the Y intercept for answer choice, eh? Just write down. So a is why Ikuo 17.4 x plus 0.22 Mansour Choice B is why equals 0.22 x plus 17.4. Easy way to select between these two is just look at our wine or so so are y intercepting the graph looks like it connects summer between 17 and 18. So that means our winer said the only one that matches would be answered. Choice B cool

Nick Johnson · Answer

So here we want to evaluate the expression X over X plus two when X is equal to negative three and when y is equal to, well, sex. So we just have well have vaccinated threes. We have negative three, divided by X plus two. So it&#x27;s state of to be divided by negative three plus two, which is equal to around negative three over negative. One native three over negative one is equal to a positive three. It&#x27;s expression evaluates to three.

Heather Zimmers · Answer

here we have the model for the population of Orlando T equals zero is your 2000 and the population is in thousands. So when we see 1656.2, we need to multiply that by 1000 and that would be the population in the year 2000. So we&#x27;re told that the population in the year 2005 is 941,000. In other words, 1.94 million. And we want to use that piece of information to find the value K in our model. All right, so let&#x27;s put 1940 into the population and let&#x27;s go ahead and put five in 40. We can solve her K. We&#x27;re going to divide both sides of the equation by 16 56.2. And if your calculator can reduce fractions for you, this is a perfect opportunity. I end up with 9700 over 8281 for that fraction. Okay, Next we want to take the natural love of both sides and then divide by five and we&#x27;ll have K by itself, not the most user friendly numbers, but we just have to do the best we can keep track of detail. Okay, So that number will go into our model every time we use the model in the next part of the problem. Now we see that the population is increasing. We see that in two places. One because the K value is positive and also because the population in the year 2005 was greater than the population in the year 2000. So now let&#x27;s use this model to find the population in the year 2010 and the year 2015. So for the year 2010 we&#x27;re going to let t equal 10. And we&#x27;re going to use our model. Why equals 16 56 0.2 times he raised to that K value that we just found Times 10. And that whole thing goes in the calculator. Now we get approximately 2272.4. Remember that 1000 people? So that&#x27;s actually 2.2 million people. And for the year 2015 we&#x27;re gonna let t equal 15 and we go through the exact same process and we have a 15 for the time, and that goes into the calculator and we get approximately 2661.8 1000 people, which means basically another 2.6 a 1,000,000 people. And then, in order to determine if the results were reasonable, I think we would need to know some more things about Orlando at the time, whether or not it makes sense for them to keep growing at this kind of rate. Uh, often, it&#x27;s not reasonable to use a model very far beyond the range of initial time. So I know the model was made for the year 2000 through the year 2007. So chances are it&#x27;s not super practical, very far beyond that. OK, but for part C, we&#x27;re going to find the year. When the population reached 2.2 million noticed that it was already above 2.2 million in the year 2010 so I would predict it&#x27;s slightly lower than 2010. Maybe 9 4008 were about to find out. So we&#x27;re going to put 2200 for the y value because that would represent 2.2 million. If you take 2200 times 1000 you get 2.2 million back was into the function and then we still have our K value and they&#x27;re and this time the unknown is the time. So we&#x27;re solving for tea. So let&#x27;s divide both sides of the equation by our initial value. And then we&#x27;re going to take the natural log of both sides. And that&#x27;s going to look like this natural log of 2200 over 16 56.2, not worrying about simplifying that just because there&#x27;s a lot of numbers to think about here. We don&#x27;t need to also simplify everything, especially with since we&#x27;re about to put it in the calculator anyway, now to get t by. So let&#x27;s divide both sides of the equation by this fraction. Even better, let&#x27;s multiply by its reciprocal so five over the natural log of 9700 over 80 to 81 times a natural law of 2200 over 16 56.2 will give us the time, but that in the calculator and we get approximately eight. So that tells us that the population reached 2.2 million in the year 2008

Problem

According to the correct model, the population of…

Problem 38 Easy Difficulty

Answer

C

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