5

The concentration C of a certain drug in a patient's bloodstream minutes after injection is given by the equation below: s0t +2 + 25Determine the time at which...

Question

The concentration C of a certain drug in a patient's bloodstream minutes after injection is given by the equation below: s0t +2 + 25Determine the time at which the concentration is highest: minutesFind the horizontal asymptote of C(t)_ Y =What happens to the concentration of the drug as increases? The concentration of the drug Select as time increases;

The concentration C of a certain drug in a patient's bloodstream minutes after injection is given by the equation below: s0t +2 + 25 Determine the time at which the concentration is highest: minutes Find the horizontal asymptote of C(t)_ Y = What happens to the concentration of the drug as increases? The concentration of the drug Select as time increases;



Answers

The concentration $C$ of a certain drug in a patient's bloodstream $t$ minutes after injection is given by $$C(t)=\frac{50 t}{t^{2}+25}$$ (a) Find the horizontal asymptote of $C(t) .$ What happens to the concentration of the drug as $t$ increases? (b) Using your graphing utility, graph $C=C(t)$ (c) Determine the time at which the concentration is highest.

So we are looking at a word problem where they have given us this equation. They're just talking about the concentration of a drug in a patient's bloodstream after 10 minutes. So the first thing they've asked us to do is find the horizontal ascent. Ope. Now the horizontal ascent. Okay. Because my degree is bigger on the bottom. Could only be at Y. Equals zero. Um There is a value for zero here. So what this assassin choke tells us is the end behavior of the graph. So pretty much as concentrations increase or as time increases, what this means is that concentration decreases. So what the ascent oak value here gives us is the end behavior of the graph. There is still a value um Her Y equals zero venice is using a graphing utility graft, the following function. So I'm just gonna throw, my point's been quickly onto the graph. I actually have um just so we can see it. And time in this case we're not going to have zero times. we're going to start at zero. So 00 and then one is to 1.9 and then two is 31 oh that's not 1.9. 1.9 is up here too is 32 three point or mhm and then three is 44 and then four is 4.8 and then five is five and then six is 4.9, seven is 47 eight is 4.49 nine is 4.2 and 10 is for so you can kind of see is starting to decrease over time. I've only gone up to 10. I could go further, it's going to get closer back down to one. Um So it says determine the time at which the concentration is the highest. So if we'd wanted to and we can actually use this as well and throw it in this way. If it lets me uh may or may not watch, let's see why equals mhm. The X. Divided by X. Squared mm plus 25. So there's our graph there and you can kind of see it. We never go above five. And we can actually use our graphing technology here to pinpoint our highest time it is at five and five. So uh five minutes I am at my highest concentration. So that gives us our graph that gives us our horizontal ascent open. Talking about what are concentration does as time increases. And it also gives us the time at which water highest dose.

Hello. Ah, In this task we have to explore the function which represents time, dependence off the concentration. So first of all, we need to find the horizontal s entered. In order to accomplish this task, we have toe start. We have to find the limit off the function when time approaches infinity. So when the time approaches infinity, Um, the function limit is zero because ah, denominator off this fraction growth faster than the nominator because the denominator is presented by square time while denominator is only linear function off time. So therefore the horizontal a similar roads is C equals zero. Then we need to sketch the we need to sketch the function. So I I just calculated the function in excel and then plot it in graphical software. So it represents Yeah, the function is represented by the maximum which we go into calculate and as well we can see that it has a horizontal assented. C equals zero. So this is that seems like, um lastly, we have to find and ah, time at which concentration reaches its maximum. So in order to do it, we have to calculate the derivative of the fund concentration and then find when this derivative equals to zero. So the derivative off the function is shown here in the in the slide. So it equals to one minus two square over to the square, plus one all square. So and this function equals to zero when nominator when the nominator equals to zero. Therefore okay, in time there yeah, therefore t equals two plus minus square would off 0.5 hours. But as we know, time is positive. Therefore, there is only one solution which is square root of 0.5, which is 0.7 hours. Therefore, the answer the question see, is that consideration reaches maximum when time equals to 0.7 hours.

We have the function C. Of T equals two T over t squared plus 100. For part A. If this function is one for 30 minutes, we want to know what's the concentration after one minute. So that would be T. Equals one. So let me see of one which would be two times 1/1 squared plus 100 or two over 101 or about 0.198 And her part B. We want to know after an hour or that will be T. Equals 60. So we really want to find sea of 60 which would be two times 60/60 square plus 100. And that is about 0.3 to four for part C. Five hours. Well after five hours that would be a T. Value of 300 300 minutes is five hours. You know like the way that looks three under. There we go. So see of 300 would be equal to two times 300 over 300 square plus 100. And this comes out to about 0.7 Uh huh. Okay. Yeah. And for part D. Since the degree of the numerator is smaller than a degree of the denominator degree one degree too. Then the horizontal aspect to it is zero. Yeah. We would expect to concentration to be zero after several days.

So I'm going to answer this question about the concentration and the bloodstream of something in particular. So t is in seconds and sees the concentration actually tears in minutes. So we're going to put one in for tea and we're going to end up with groups to over 101. And when I divide that on here too, divided by one oh one, we're going to get 0.198 Now we need to do it in one hour, which means we're going to put 60 minutes in there. So we're going to have 120 all over 3700. So 120 divided by 3700. And that's going to give us 0.3 to four. And then we're gonna do five hours, which is 300 minutes. So we have two times 300 over 300 squared plus 100. So we have 600 over 1000, which is really 6/10 0.6. And then we're going to look for the horizontal ass in tow and the horizontal essential for this one, this one's bottom having the bottom is growing faster, so the horizontal ASuntos is X equals zero. So after several days, what do we expect the concentration to be? We expect it to be approaching zero. Mhm.


Similar Solved Questions

5 answers
3) Here is another way to prove that there are infinitely many primitive pythagorean triples_ I a? + 62 and GCD(a.6.c) pruie that mlust be odd aud exaetly one of or b MuSt be eren: Suppose that is even: Next consider a? 67 = (c +b)(c 6) . Study this equation usiug uhique factorization:
3) Here is another way to prove that there are infinitely many primitive pythagorean triples_ I a? + 62 and GCD(a.6.c) pruie that mlust be odd aud exaetly one of or b MuSt be eren: Suppose that is even: Next consider a? 67 = (c +b)(c 6) . Study this equation usiug uhique factorization:...
5 answers
Identify 5 What: WOJJ the 210 Thirty-five type . = HH 5768 used? H sanad3 321 329 history majors H selecied
Identify 5 What: WOJJ the 210 Thirty-five type . = HH 5768 used? H sanad3 321 329 history majors H selecied...
5 answers
What is the Noilsano density of an objecr of mass 2 and volume 2 45 in units 'ol kolm ?
What is the Noilsano density of an objecr of mass 2 and volume 2 45 in units 'ol kolm ?...
5 answers
4ele 4Sl 9Fnie Question: 10 pts Find (a) the range, and (b) the standard deviation for the given sample_ 85.75, 84.84 85.66 85.66, 84.13 85.07 85,94 84.92, 84.57(a) Find the range of the given sampleRange (Simplify your answer: Type an integer or & decimal ) (b) Find the standard deviation of the given sample_(Simplify your answer: Type an integer or decimal rounded lo Ihe nearest hundredth as needed )
4ele 4Sl 9 Fnie Question: 10 pts Find (a) the range, and (b) the standard deviation for the given sample_ 85.75, 84.84 85.66 85.66, 84.13 85.07 85,94 84.92, 84.57 (a) Find the range of the given sample Range (Simplify your answer: Type an integer or & decimal ) (b) Find the standard deviation ...
5 answers
F u weight ix hung from TpC, thee more tension in te rope ifit is strelched horizontally than if it 1 slrclched vcrtically bccausethe rcaction force 0n vettical rope cancels out the weight 8 sincc the horizontal rupe is bcing pulled from both ends; it has more tension C cch side of & vertical rope carries only half of the wcight OD.a ncarly horizontal rope needs more tension t0 create the same upward supporting force
F u weight ix hung from TpC, thee more tension in te rope ifit is strelched horizontally than if it 1 slrclched vcrtically bccause the rcaction force 0n vettical rope cancels out the weight 8 sincc the horizontal rupe is bcing pulled from both ends; it has more tension C cch side of & vertical r...
4 answers
15) Given the reaction: Nxe - Oztd)2nOW Kc -4.7*10 31If the equlllbrium concentration of Nz Is 10* 10 * Mand the equlllbrium concentrat cqullibrium concentration of NO?0 19 * 10*0 14 * 10 #45 * 10 !00 4 x 10 1 M0 70* 101Questan 1616) For thc hrst Ordtr reacnon ? Hir = 2 Hzo + 2k2 1.80 K 10 J } /sec.Vi enc Indz| conccntrztion 0i HI i 0.90 Mhow Jong would It take tor thc concentrtion0 520 scond:102 econd0 88 .0 tcconds234 tecondt0 181 uccond
15) Given the reaction: Nxe - Oztd) 2nOW Kc -4.7*10 31 If the equlllbrium concentration of Nz Is 10* 10 * Mand the equlllbrium concentrat cqullibrium concentration of NO? 0 19 * 10* 0 14 * 10 # 45 * 10 !0 0 4 x 10 1 M 0 70* 101 Questan 16 16) For thc hrst Ordtr reacnon ? Hir = 2 Hzo + 2k2 1.80 K 10 ...
5 answers
The four sequential sides of quadrilateral have lengths a 45,6 = 7.7, € = 8.9,and d = 1L.3 (all measured in yards). The angle between the two smallest sides is a = 105What is the ared of this figure? areaQuestion Help: OvidsoSubmit Question
The four sequential sides of quadrilateral have lengths a 45,6 = 7.7, € = 8.9,and d = 1L.3 (all measured in yards). The angle between the two smallest sides is a = 105 What is the ared of this figure? area Question Help: Ovidso Submit Question...
5 answers
Express the equation in logarithmic form_ 32-4/5 0625
Express the equation in logarithmic form_ 32-4/5 0625...
5 answers
Solve the equation.$$ rac{2}{3 x}+ rac{1}{2}= rac{4}{x}+ rac{4}{3}$$
Solve the equation. $$\frac{2}{3 x}+\frac{1}{2}=\frac{4}{x}+\frac{4}{3}$$...
1 answers
Determine whether each statement can be assumed from the figure. Explain. $\overline{A B} \perp \overline{B C}$
Determine whether each statement can be assumed from the figure. Explain. $\overline{A B} \perp \overline{B C}$...
5 answers
(3) Solve y(6) 9y(5) +39y(4) 125y(3) + 294y' 396y' + 216yl
(3) Solve y(6) 9y(5) +39y(4) 125y(3) + 294y' 396y' + 216yl...
5 answers
Find the I(t) with 1(0) = Xo for the stochastic differential equation:dIt =sin 2It + 3 sin41) dt + cos? Xt dWtwhere t satisfies some suitable condition_
Find the I(t) with 1(0) = Xo for the stochastic differential equation: dIt = sin 2It + 3 sin41) dt + cos? Xt dWt where t satisfies some suitable condition_...
5 answers
The contour map for function f defined on the square [0 , 2 function is estimated to be[0, 25 is shown in the following figure. Using the Midpoint Rule with m = n = 2,the average value of the
The contour map for function f defined on the square [0 , 2 function is estimated to be [0, 25 is shown in the following figure. Using the Midpoint Rule with m = n = 2,the average value of the...
5 answers
Identify the conjugate bases in the following reactions_HHe CH;-N-H HCH:_N-HCH:CH:- ~C0-HCHs CHz,&-HNa HCH: CHz 0:NaH_HIVCH:- ~0-HH-CI :CH;-O-H HClVI
Identify the conjugate bases in the following reactions_ H He CH;-N-H H CH:_N-H CH: CH:- ~C 0-H CHs CHz,&-H Na H CH: CHz 0:Na H_H IV CH:- ~0-H H-CI : CH;-O-H H Cl VI...
5 answers
(4pts) cotassiurn thiocyanate, describe the reactant appearance and identify the evidence of For the reaction af iron(IIl) chloride = reactlon Then balance (he chemical equation end Identify the lype of reaction chemica Xixi- EI== 6x101012 8126/913i Hormdi B / I | VCFtcnitocnemcnnreactcnRroctunt wppc_narcoEaceniFecl(om)KscN(TUanceFech(o?}KsCKi4GFe(SCNJa(44) + KLIqILype Ueacinn
(4pts) cotassiurn thiocyanate, describe the reactant appearance and identify the evidence of For the reaction af iron(IIl) chloride = reactlon Then balance (he chemical equation end Identify the lype of reaction chemica Xixi- EI== 6x101012 8126/913i Hormdi B / I | V CFtcnitocnemcnnreactcn Rroctunt w...
5 answers
Suppose log 62=a and log 63=c Use the properties of logarithms to find the following_ log b36bJog 36b
Suppose log 62=a and log 63=c Use the properties of logarithms to find the following_ log b36b Jog 36b...

-- 0.019936--