Math HL IA Type II - Modelling the Course of a Viral Illness

i really need help on this. i've managed to do the first 3 questions but i'm stuck on Q4,5,6 & 7. pls anybody? i'm not begging for answers [not that i'll turn them down at this stage, lol] but maybe suggestions to solve the questions? help :confused:

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Reply 1

smilies

Sorry to drag up an old thread but I'm doing the same IA and seemed to have hit a wall on part 3... I modelled it as:

Q = Qo*1.6^(t/4) - (1.2x10^6)t

where Q = no. of viral particles in the body at time t, Qo = initial number of viral particles in the body at time t.

For recovery, Q must = 0, so if I rearrange the eq. to find the highest value of Qo when Q=0, it should lie between 9 and 10 million, as the question suggests. However, when I graph this, I get a value between 3 and 4 million - a few others, including my teacher, have got the same result. Is there something wrong with our method?

Thanks :smile:

Reply 2

jc_bach

you shouldnt plot it in a graph, instead you need to solve it using algebra, then use log to find the answer

Reply 3

smilies

But if t and Qo are unknown, how can I solve it algebraically?

Reply 4

jc_bach

your equation is sufficient to solve the question, just dx/dt it and find (in what symbols you have), Qo, using simple algebra (switching the sides as to say)

Reply 5

sadhukar

jc_bach

your equation is sufficient to solve the question, just dx/dt it and find (in what symbols you have), Qo, using simple algebra (switching the sides as to say)

Hey, I got the first part alright, but for question 4 is it just a linear equation? I have a feeling my solution was too easy.

note: sorry for PM'ing, you was worried you might not notice >.>

Reply 6

jc_bach

first solve it as a differential equation (find it yourself), integrate it and substitute the given numbers t=0 M=0, t=4, M=90
then you can find the solution, its that easy.

Reply 7

sadhukar

jc_bach

first solve it as a differential equation (find it yourself), integrate it and substitute the given numbers t=0 M=0, t=4, M=90
then you can find the solution, its that easy.

I'm sorry but what...

I just made a linear graph t = 0 to 4, m = 0 to 90 and drew 2 dots on the end and connected them. Then I find out the amount needed to add each hour. That sounds wildly different to what you described :s-smilie:

Reply 8

Shekstar

you can use it using integration, like u used in the first few questions - set up an equation for rate of increase of medication with respect to time, and the integrate it

Reply 9

Shekstar

sadhukar

problem with that is that your method is discrete, and not continuous - the question had continuous in bold, so just assumed u need calculus

Reply 10

jc_bach

duh it is not a linear graph it is an expodential graph coz you didnt count the elimination by the kidney.
and i said find the differential equation yourself, so do it.

Reply 11

slayer845

um for the modelling infection Q2 did anyone get t=117.6 hours
just wondering if im on the right path. and how would i find the dx/dt of the function i found in 3?

Reply 12

jc_bach

thats the wrong model you need to use another model (although the answer is close to yours)
for q3 find the equation for the no. of viral p. for the next hour.

Reply 13

la_1

I need help with question 4, it's such a pain, I can't seem to figure out the formula to then differentiate :frown:

Reply 14

jc_bach

think differential equation.
I cant guide u that much.

Reply 15

slayer845

hey jc_back.
yeah for Question 4...i had an idea where you could possibly use the formula for continuous compound interest...and if I do that..i dont think you even need to use calculus.

The formula for the compound interest is: y = (initial)*(e^(rt))
initial = 90 micrograms? is that the initial or does that have to be the initial viral particles...(10,000)
r = rate (we don't know)
t = time (we know is 4 hours)

and now if we factored in what is happening with the kidneys...its eliminating of whats left..would it be like:
y = 90e^(4r)-e^((1-2.5%)*4)

otherwise i dont know how the hell to do 4...please PM me :frown:

Reply 16

jc_bach

first spell my name correctly.

Reply 17

jc_bach

its not initial it is the constant k which is the amount of medicine enter to body per hour.
and firstly i CLEARLY SAID THINK Differential Equation.

Reply 18

la_1

i finished it!
wahoooooooooooooooooo!

Reply 19

vbvanc

guys!
...
i need help with number 1!! i don't understand what to do..because if i use the compound interest formula, i don't know what to fo with the "-1"

compound interest eq:
u(sub n) = u(sub 1)r^(n-1)

where u(sub n) is the number of particles after n hours,
u(sub 1) is the initial number of particles,
r is the geometric ration (in this case 2 because it doubles)
and n is (t/4 ???)

thank you

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Math HL IA Type II - Modelling the Course of a Viral Illness

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