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Resultsi1. Using one sheet of standard (non-logarithmic) graph paper, plot the OD 600 on the vertical axis versus time (minutes) on the horizontal axis for each o...

Question

Resultsi1. Using one sheet of standard (non-logarithmic) graph paper, plot the OD 600 on the vertical axis versus time (minutes) on the horizontal axis for each of the four tubes. Place all four curves on one graph Using the starting and ending OD values_ calculate the OD/min. for each tube: Note: The plots are not usually linear; thus exact slopes are difficult to determine. Construct table 2 to specify the OD/min for each sample:OD/min ((OD start OD finall/total minutes of assay)Calculate th

Resultsi 1. Using one sheet of standard (non-logarithmic) graph paper, plot the OD 600 on the vertical axis versus time (minutes) on the horizontal axis for each of the four tubes. Place all four curves on one graph Using the starting and ending OD values_ calculate the OD/min. for each tube: Note: The plots are not usually linear; thus exact slopes are difficult to determine. Construct table 2 to specify the OD/min for each sample: OD/min ((OD start OD finall/total minutes of assay) Calculate the specific activity for tubes 1-4. Average the specific activity for the mitochondrial suspension fraction (tubes 182) and for the negative control fraction (tubes & 4) Specific activity for tube 1, 2 = (OD/min)/(ug/ul of protein for mitochondrial suspension fraction) Specific activity for tube 3,4 = (OD/min)/( ug/ul of protein for negative control fraction) Stop and evaluate your results: The calculated specific activity is used to determine which fraction tubes &2 or 3 & 4) contains the highest mitochondrial concentration: Tube one and two theoretically should be higher based on the differential centrifugation scheme.



Answers

A certain drug is administered intravenously to a patient at the continuous rate of $r$ milligrams per hour. The paticnt's body removes the drug from the bloodstream at a rate proportional to the amount of the drug in the blood, with constant of proportionality $k=.5$ (a) Write a differential equation that is satisfied by the amount $f(t)$ of the drug in the blood at time $t$ (in hours). (b) Find $f(t)$ assuming that $f(0)=0 .$ (Give your answer in terms of $r .)$ (c) In a therapeutic 2 -hour infusion, the amount of drug in the body should reach 1 milligram within 1 hour of administration and stay above this level for another hour. However, to avoid toxicity, the amount of drug in the body should not exceed 2 milligrams at any time. Plot the graph of $f(t)$ on the interval $1 \leq t \leq 2,$ as $r$ varies between 1 and 2 by increments of $.1 .$ That is, plot $f(t)$ for $r=1,1.1,1.2,1.3, \ldots . .2 .$ By looking at the graphs, pick the values of $r$ that yield a therapeutic and nontoxic 2-hour infusion.

For the first part. Looking at the given graph, we can estimate that after three hours, the concentration in the blood is approximately 1.5 1.5 milligrams per leader. Now let's go ahead and use the function given to us to see how accurate we are. So that will be five times three over three squared is nine plus 10 and in fact that is so nine plus one. And that is in fact 15/10 which is 1.5. And using taking a look at the equation the horizontal Assen towed here. If you look at the degrees of the numerator and the denominator, the degree of the denominator is greater. So that tells us that the horizontal Assen tote will be at y equals zero.

Hello. So here we have the function C. F. T. Is equal to five T. Divided by T squared plus one. So here CFT represents a drugs concentration in milligrams per liter after tea hours. So the graph of that function um is gonna look while something like this here. Nothing to graph we can see that a reasonable estimation for the drug concentration after three hours. So when this is the T. Axis basically here on the X. Axis. So in T. S. Three we hit the graph about 1.5. So after three hours we can say um reasonable estimation is going to be 1.5. So that's the part A. Then for part B. Um We then consider the equation C. F. T. Five T. Over T squared plus one. Now here we're going to replace three with key in our equation and we're gonna evaluate sea of three. So see of three. That's going to be equal to five times three and then divided by three squared plus one. So that's going to be 15 divided by nine plus one. Right? That's going to be 15/10 which is 1.5. So again the drug concentration after three hours we can say is 1.5. Um And that's in milligrams per liter. Uh huh. All right. And then for parts seat again we consider our equation C. F. T. Which again is equal to five T. Over T square plus one. So the degree of the numerator here um is one which is less than the degree of our denominator which is two. So therefore the graph this of CFT has as the X. Axis as we conceive the graph as a horizontal ass from tow. Therefore, um the equation of the horizontal at santo is going to be well C. F. T. Is equal to zero. Yeah. All right. And we can say that the drug concentration in the patient's bloodstream is going to approach zero um As as T gets larger and larger.

Okay, so for part a time, zero with equal zero. Um, so right deep again zero that see on the products just commit the whole expression. Zero. That makes sense. Because, like, right when a drug is administered, like even if it's injected or orally taken in No, we don't know. Um, it has an ad zero time. It's just sitting right where it left the needle of right where the pill is. Um, so at T equals zero. The amount is equal to zero. So just makes sense because it just hasn't had time to get into the bloodstream yet. OK, Part B must know how much is in there after one hour, and so there is going to be 3.42 milligrams per liter of drug concentration. Came part C wants me to sketch a graph of this function so all that really matters is positive time values and positive amounts. So this graph starts at 00 It's gonna go up and then back down as t approach isn't me on the maximum of this one is kind of close to 3 a.m. Every 3.5. Okay, So I d, uh, it levels off to as t approaches infinity, the amount, the concentration. I guess I should market this. No capital C that C is gonna be approaching zero. That makes sense in context, cause your body and your liver start processing it out. So the fact that it never quite gets to zero I mean, at some point, I guess there's always gonna be, like, one little dot of it in your system. But because it's like discrete numbers of Adam's, eventually it will be completely out of your system. And so, uh, party Okay. So funny when it reaches its maximum. So I'm just using the maximum notation. Mr the Time is gonna be actually 3.636 when it reaches its max. Uh, hours. Okay. And then, uh, I'm gonna also plot the line y equals, uh, three milligrams for leader. Just y equals three. And then just find where that intersects the ground. The second time in intersects the graph is gonna be 9.759 hours later will be the second time. It's at three milligrams for leader. Okay, thank you very much.

Here in this problem were given with differential equation, which is M frame d Bless g times A mufti is equals toe I and where a mufti is the mars of the drug on K represents the constant and I is the infusion rate on their three parts given in equation and the A pot. They're asking to verify that the solution of this initial value problem is MFP is equals toe. I divide by k times one minus either the power minus Katie on the initial condition given is em off. Zero is equal to zero on initial condition ratings went d zero We get m as Zito so we'll be start proceeding with the result over the a part. So in they but very five for out of your calculate m frame t from dysfunction timeframe t will be equals two. I've a case constant We can dig outside and here one is different Asian off one will be zero because it's a constant minus differentiation off, hear about minus Security will be here to about minus scary times minus key. So it will become Bless K after a simplification will get the result as i Times unit about minus Katie. So this is a village lately or praying for and prime D. Now we're going to subservience value in this differential equation. So for that, I will be taking the left side off the differential equation. So I'm frankly, that we have calculated Is I a times you did about minus kitty bless care times a mufti were given with I divide by K times one minus unit of our minus Katie. So we'll get I bless i times about minus Katie Bless skincare Cancel out. So I times one minus. You did about minus Katie. Again, we'll simplify. So I at times heated about minus Katie. Bless every get I minus. I hear about minus Katie. These two normal cancel out on we're left with eye on this is equal to artists Hence, via verify that the given function is a solution of the given initial value problem. Now, in a be part on immigration, they're asking it. I is there a telling their eyes equals two pain Milligram per hour and K is equal to 0.5 per hour on were to graft the solution. You know the solution is a mufti is equal to I divide wakey one minus. You did about minus Katie, some believe, able to plug the values in this function. So I enlist in the ride back Here is 0.0 Fife one minus beautiful, minus 0.5 times t. So offer simplification will get 200 times one minus here the bone minus 0.5 times Steam on this will be gold and more free. We have to graft dysfunction. But I got office people and we can use a graphing calculator also. So let's grab this function. So this is a collaborative opened on this X is a mufti on this one. ISTEA on discover presents the equation mostly is equals to 12 200 times one minus beauty about minus 0.5 50. So this is answer for the be part on this Eve part. They're asking to find the really off limit he tends to invite and must be So I'm off TV no is equal to I Divide by K. Times one minus. Here. The power mine minus Katie. So we're going to evaluate this limit so limit to dance to invite most Please wonder I divide by K one minus beautiful minus kitty. I simply go to plug element so limit he tends to invite I divide wakey one minus beauty about minus. And for nighttime, steep. So we know that you did about minus In finite time Steve will be equals to one divide by You're the boss. Invite invited James D. On this will be able to wonder whether in freight it comes out to be a zero. So finally the answer for this limit will be I divide by key Onda. We're also very fired this with the graph. So if you see carefully in their day, I is giving us in the be part. It is given us 10 milligrams per hour and he's given us 0.0 Fife. But over you have blood these value Here we get 10 divide by 0.5 and that comes out to be Yes, I wondered. So figured em off. Diaz 200 on At T equals in fight same thing and we referred from the graph also that when a mufti approaches 20 approaches infinite, we get the value of a mufti s 200. This can be verified from the graph also. So the final answer I hope you with a problem. Thank you


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