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# IB Math HL Portfolio... watch

1. If anyone is doing MAth HL...I have just been given a type II portfolio on modelling the course of a viral illness and its treatment. It is due in a week, and i have no idea what to do! I know it is something to do with exponentials/ logs etc but i have no idea where to start! Any help would be really appreciated!
2. yei! i have that portfolio assignmnt too!pitty i cant help cause i really don´t know how to do it...you´r not alone.
3. hey... so what did you do in the end? mine's due this friday and I could need some help... thanks
4. Can't tell you how or what to do. That would be a breach of Academic Honesty. But if you take the question carefully and systematically, you should do fine.

Go over the markscheme. See what it wants, and follow it. Make equations or values to model and then talk about them.

Hope that helps!
5. To be honest it doesn't... I'm not asking for the answer, just how I should get started.
6. i've done that one. can't really tell you exactly what to do but basically, this is the idea:
the first few parts are really easy, building a simple equation (equation) that fits the rate of virals, solving it to find the time for immune to respond. Excel he formula or otherwise t to find the "death time". Equate equation to the rate of medication to do the next part. The later bit involves integrating rather complicated differential equations.
Not sure if i have told you enough or too much. But good luck on starting it.

p.s. I think one hint is, always build "continuous models" that is not discrete for this portfolio.
7. well, we are doing the same one now,,
my first modell for the infection was something y=10000*e^0.1733x, and also another one which is y=10000*2^(x/4)

the first equation was from excel, the second was using geometirc series equation !!

thats what i have now !!
8. hey... i have the same question... i got stuck on number 6.... it seems too similar to number 3... And I have no idea what to do for number 7 either.... can someone please tell me what questions number 6 and 7 are asking for so that i can get started???
9. Okay, so the problem exists within continuous time, but surely to model it as a discrete problem with a sufficiently small time interval (per second, maybe) should suffice? Certainly our answer will be well within tolerable bounds. I thought this task was good fun. Any questions?
10. Hi everyone,
I am attempting this Math IA, too. I got through q1 ok, but now I am stuck on q2 (which is really sad, I know). My thought on this is:
I was trying to find a formula, so that I can find the time for which the # of viral particles equals 10^12, which is when the person dies.
In number 1, I found out that the time at which the immune response begins. (I will try to make this as abstract as possible, so that no-one can copy...). I then had this formula:
something is wrong with my equation, however. When I find the values with an excell chart, this is what I did:
V(t)=1,000,000*1.6^(t/4)-50000t, where t is the time that passed from the time when there were 1,000,000 particles in the body.

Thank you so much for your help
11. Hi everyone,
I am attempting this Math IA, too. I got through q1 ok, but now I am stuck on q2 (which is really sad, I know). My thought on this is:
I was trying to find a formula, so that I can find the time for which the # of viral particles equals 10^12, which is when the person dies.
In number 1, I found out that the time at which the immune response begins. (I will try to make this as abstract as possible, so that no-one can copy...). I then had this formula:
something is wrong with my equation, however. When I find the values with an excell chart, this is what I did:
V(t)=1,000,000*1.6^(t/4)-50000t, where t is the time that passed from the time when there were 1,000,000 particles in the body.

Thank you so much for your help
12. Hi Sinaw,
The rate at which the particles change is proportional to the number of particles. So, dP/dt = kP, where K is a constant. Solving this will lead you to P = 10000e^(kt). Using the initial conditions of P=20000 when t=4 should lead you to establish k=0.25ln2. Now let P=10^12 and solve the equation for t. Hope this helps.
13. Hi Sinaw,
Re: last message.
k=0.25ln2 for part 1.
In part 2 I think you need k= 0.25ln1.6.
Sorry.
14. Hi Sinaw,
Re: last message.
k=0.25ln2 for part 1.
In part 2 I think you need k= 0.25ln1.6.
Sorry.
15. Hey Sciortino,
thank you so much for your help! Because it wasn't working and I just now saw your post, I modeled #2 by using a spreadsheet, like it said in the question. It actually turned out to be quite easy that way
But your suggestion to find the equation with the derivative and then integrating is definitely a good idea that I will keep in mind for the following questions. This will probably help me a lot on #4, I think..
Now I am stuck on #3. ( and I have the feeling that I will continue to be stuck on every question )
The idea that I had was setting up an equation, finding the derivative and setting it equal to zero. Does that seem right?

16. Hello Sinaw,

So sorry for the delay in replying - been hectic!

Re: Part 3. I bet you've solved it by now. Your idea seems sound to me. Let P be the required number of particles. Therefore P*e^(0.25ln1.6) - 1200000 < 0. Solving this (use solver on the calculator, if necessary) will bring out the required P value.

Best wishes,

Antonio Sciortino.
17. Hi Sinaw,

Been thinking about Part 4 - I wondered about a discrete model here.

If A goes in smoothly over a 4 hour period then A/14400 goes in every second!

However, the proportion 0.025/3600 is excreted per second, meaning that R = 1 - 0.025/3600 remains.

Using the formula for the sum of a GP with R as the first term and the same R as the common ratio and t =14400 must give an amazingly accurate solution.

Try it!

Antonio Sciortino.
18. hi, um for question two did u get roughly 120hours (4 wem they die without meds) ????
frm 'in need of serious help'
19. wait, forget my previous post, it was wrong.
20. hey guys.. can u help me maths hl portfolio type 1 topic 2 INVESTIGATING RATIOS OF AREAS AND VOLUMES...!! i need help in question 2 Does your conjecture hold only for areas between 0x and 1x? Examine for 0x and 2x, 1x and 2x, etc.

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Updated: December 28, 2009
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