the-population-of-st-petersburg-florida-in-thousands-can-be-approximated-by-the-function-gx-12798191

Question

The population of St. Petersburg, Florida (in thousands) can be approximated by the function
$$
g(x)=-127.9+81.91 \ln x \quad(x \geq 70)
$$
where $x=70$ corresponds to 1970
(a) Estimate the population in 1995 and 2003 .
(b) If this model remains accurate, when will the population be $260,000 ?$

Himanshu Kushwaha · Accepted Answer

we have given the population off. ST. Petersburg, Florida Given by the function, G off X is equal to minus 127.9 plus 81.91 load off X, where X is greater than equal to 70. In first part, we have to find the populace, and in 1995 and 1/2 then three so G over 95 will be equal to minus 127.9 plus 81.91 Look over 95 we get the polka. Listen is 245.10 1000 and Z off. Wendy Rotary estimates in 2000 into how gentle terry the populace and will be four to minus one under 27.9 plus 81.91 low off 130 Vega. This is equal to or 251.7 3000. So input elementary this much it&#x27;s the pope. Listen, in second part, we have been asked that if the mortal remains correct, then man will the hopeless and will reach to like 60,000. It means we have to solve wonder 60 with minus 127.9 plus 81 point 91 Law off X. And when we saw this vigor X is equal to 140 being bed in these days, the but listen will be to like 60,000.

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

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

Ankit Gupta · Answer

in this question, we are given a 50 equal to 25.1, divided by one plus 2.7 multiplied with a to the power minus 0.5 multiplayer with teeth. No, in the first part off the question it is Ask that what was Florida&#x27;s population in 1970? That means in 1970 t is equal to zero because that is the start. Only now, by putting equal to zero bigot f of zero equal to 25.1, divided by one plus 2.7 e to the power minus 0.5 multiplied of it. Zero. So we get f off. Zero is equal to 25.1, divided by one plus 2.7. Now he to the part zero will be one. So we get it as 25.1, divided by 3.7. Solving it we get f zero is equal. Do 6.7 approximately now in the bleep part off the question we have to tell its population in 2010. That means from 1970 to 2010 K is equal do 40 so we will put the value of two years. 40 Forget F or 40 as equal to 25.1, divided by one plus 2.7 into the par minus 0.5 multiplied with 40 and for four table become equal to 25.1, divided by one plus 2.7 multiplied with E to the power minus two. So F or 40 is equal toe, 18.38 approximately so it always estimates this now in the sea part off the question it is asking from Munster limiting size off the population. And we know from the function given as a 50 equal toe, 25.1 divided by one plus 2.78 the par minus 0.5 50 We know that the constant in the numerator that is C 25.1 does our stand limiting saying so. The limiting size is 25.1

Edward Downes · Answer

Okay. This question gives us a logistic model. Says that he is the years since 1990 and he is the population of the world in billions. So we noticed we have a logistic model right here. We&#x27;ve got the logistic model with the unknowns in right here. Hey, First part of the question, I says, what is the maximum sustainable population for the world? So we know that this is the limiting factor of the carrying capacity for the population, which is going to be the l on top here. So just matching these two equations up, we can see very clearly the elbow equal 40. This is the question said his billions of people. So the carrying capacity to maximum sustainable population of the world will be about 40 billion. Bye B s is too graft dysfunction p against T so we can throw down a quick little graph here. We know the general format of a logistical models that tea is our independent variable. He is a dependent variable. The population now we know from pot, eh, that the maximum sustainable population will be in about 40 billion. So a logistical model will not go above that okay, and it will follow the general logistical shape. Okay, so when Tea Kool zero, we know that we&#x27;re gonna end up with P as 40 over one plus 11. And then this will be easy to the power zero cause that time is Sierra. Anything to the power zero we know is one. So when t zero, our population will be about 40 over 12 which you can calculate to be about 3.3. That this will kind of service are why intercept or a P intercepting escapes. Population is starting at about 3.3 Ryker, I think we&#x27;re gonna go for about 100 years. We&#x27;ve got out P access already nice and scans that we know that it will follow religious shape. We&#x27;re growing and then the population will slow down and it will approach this carrying capacity oldest limiting value. Right now. According to this model, when will the US population B 20 billion in 39.3 billion. So we&#x27;re putting in for our P values. Pecos 20 and then p equals d 9.9. So we need to solve each of these. So it&#x27;s substituting these in for you, but we&#x27;re gonna solve the tea here. Hi. So two ways we can do this. The 1st 1 is algebraic. The 2nd 1 is using up graph. I&#x27;ll do the 1st 1 algebraic Lee. So we multiply both sides by the denominator here. Thank 20 people&#x27;s one close 11 into the negative 0.8 called sporty. We&#x27;re gonna divide both sides by 20 year. We can drop the prince sees at this point before the divided by 20. We know that&#x27;s gonna give us two on that side. Okay, We&#x27;re going to subtract the one both sides to the magnets. One 11 that the exponential people&#x27;s one. We&#x27;ll divide both sides but never became so that so. Our experience Little a letter. Now we&#x27;re going to apply the natural blogger of them to both sides. So l a I love science at my school called. We&#x27;re gonna take the natural log of both sides. We know that this will cancel. Hey, think about this. Is canceling is the natural base that he way Type this in a calculator for an approximate value. A natural law one divided by 11 give you a negative two point to bring mother decimals bite off the negative 0.8 which would give us 29.9 steps. So approximately B 30 years for the population to reach 20 billion. Thank you. The second option to solve this type of problem will do this with you. Population is 30 no 1,000,000,000. You get the same kind of problem with the name out. But if we&#x27;ve got a calculated that has graphing capabilities, we can definitely get it to help us out here. Okay, we can substitute each of these equations into the graphing feature of the calculator. So I&#x27;m using a T I 84 years so I can put this one in white one that this William White too. And essentially find where these two into sex. I&#x27;ve already got this one this copy of the equation graft up here in the blue. I&#x27;m gonna graft this study 9.9. I know that&#x27;s just gonna be a horizontal line. That&#x27;s why he opposed nine by nine. And I confined this point of intersection, so that&#x27;s not too difficult for me to do if I&#x27;m familiar with the capabilities of my calculator. So just run through that real quick on the side. You guys can check it by yourself. A home. Hey. And you should get an intersection at just over 100 I believe. Give me one second one like today. The grafts, these two guys, we should get in in this section. We should find that the point of intersection is a 104 point eight and obviously the White Open. That will be 39 point. So we&#x27;re looking for the time with the Intersect, So we just take t Valiant without a full, maybe 100 and five years here.

Nick Johnson · 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.

Problem

A bicycle store finds that the number $N$ of bike…

Problem 84 Hard Difficulty

The population of St. Petersburg, Florida (in thousands) can be approximated by the function
$$
g(x)=-127.9+81.91 \ln x \quad(x \geq 70)
$$
where $x=70$ corresponds to 1970
(a) Estimate the population in 1995 and 2003 .
(b) If this model remains accurate, when will the population be $260,000 ?$

Answer

a. 251.75
b. 2014

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Thomas W. Hungerford, Douglas J. Shaw

Contemporary Precalculus: A Graphing Approach

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Continuity - Overview

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a. 251.75b. 2014

Contemporary Precalculus: A Graphing Approach

Megan C.

Heather Z.

Kayleah T.

Michael D.

Continuity - Overview

Continuity - Example 1

Thomas W. Hungerford, Douglas J. ShawContemporary Precalculus: A Graphing Approach

Megan C.

Heather Z.

Kayleah T.

Michael D.

a. 251.75
b. 2014

Thomas W. Hungerford, Douglas J. Shaw

Contemporary Precalculus: A Graphing Approach