Q5.
Q6. The exponential function y=a(bx) indicates that a: The amount of penicillin active at administration. b: Is 60% of the value before (in this case), X: represent the difference of time wanted and time of which penicillin was administrated/h.
y=300*(0.6x).
The function represents amount of active penicillin in the bloodstream at any given time need to be calculated. So if I were to calculate the amount of penicillin at 15:00 then . x= 15:00 – 7:00 = (8)
y=300*(0.69).
= 5.08 Units
Q7.
10 hours after administration the 1.81 as we can see on the graph .
y=300*(0.610). We substitute x for 10, as the difference of time= 10. The answer is 1.813985, rounded up to 3.sf 1.81mg.
Q8.
Now that we are looking at the time, after which less than 10mg of pencillin with be active after administration, we have to make y= 10.
So the equation is 10 =300*(0.6x).
But to get the time we have to make the exponent, so x the subject of the formula. Therefore, we have to proceed using logs. 10/300=0.6x
0.03.=0.6x
Log0.03./Log0.6 = x
6.86(3 s.f.) = x
6.86 Hours.
60 hours 0.86 = 51.6 minutes
60 minutes x 0.6 = 36 seconds
Meaning that after 6 hours, 51.6 minutes, and 36 seconds after administration there will be less than 10mg amount of active penicillin in the bloodstream.
9.
From the table above you can see that after every 6 hours the line decreases gradually because every hour the value is reduced to 60% of the value before, but then suddenly the line shoots back up, to averagely 314 grams, representing that the new dose has been administrated. What this shows is that every time after 6 hours this is averagely 14g of penicillin remaining in the body. But after 48 hours the amount of active penicillin left in the blood stream is reduce to 0.00149mg * see appendix (table 48 hours) .
You can also use the following formula to find out the amount of penicillin left in the body after 48 hours.
I want to see know if, any changes were to made done to the amount of penicillin administrated and the time of intervals between the doses would have affect on the amount of penciling remaining after 48 hours.
I will start by first investigating if amount of penicillin will affect. I’m going to change the administration dose to 150 grams, half of the original dose set by the doctor. The number of doses are still going to be five, or a 6 hour interval.
As you can see from the graph, that after changing the administration amount of penicillin to 150, the pattern on the gram Is still the same, meaning that after 6 hours from administration, the amount of insulin decreases gradually, and after 6 hours it rises up suddenly, indicating that new dosage has been injected into the body. But the amount of insulin is at 157 averagely, after the new dosage has been added, showing that there was still 17mg of insulin remaining from the previous dosage.
Now if we compare this to the average amount of penciling remaining after 6 hours interval it, was 14mg average in the investigation before, whereas it is 17mg remaining now. What this shows that there is a little, but still a difference of 3mg of penicillin remain more when the dosage is halved, from the original 300.
If we look at the table (see appendix “amount of insulin 150 administration) the penicillin remaining after 48 hours was 0.00746 mg. Comparing this again with the amount remaining in the experiment before, was 0.00149mg. Here we can see clearly, that yes the amount of dosage administrated does have a affected on the amount of penicillin reaming active in the blood stream after 48 hours. 0.00697mg of penicillin remain more when u half the dosage of the original administration dosage. There is a 19.97% increase in the amount remaining.
Now the final test is to see wither the change in the intervals between the dosage will have an affect on the penicillin reaming in the body after 48 hours, 2days. I will increase the interval up to 8 hours, and see how this affects.
As you can see from the graph, after increasing the dosage intervals to 8 hours, you can actually see that the amount of active penicillin remaining in the body, increased also. Thus we can say that the time of interval is proportional to the Amount of pencillin remaining in the body.
Now if we compare the remaining amount of penicillin after 48 hours from administration with a interval of 6 hours the figure was: to 0.00149mg, and for this it was 0.031914 mg. You can clearly see that there is a difference between the two, when I increased the invetervals the amount of pencillin remaining was 0.03024 mg.
Thus we can state from the results I have achieved that both dosage of pencillin administrated and the time of intervals if manipulated will affect the amount of penicillin remaining in the body after a 48 hours study.
Akash Singh
17.12.08
Appendix
Q91.
Table: Amount insulin present in bloodstream after 48 hours
Table 2: Amount of Pencillin in bloodstream after 48 hours with administration dosage of 150mg
Q9. <Table for amount of penicillin remaining after 48 hours, with 8 hour interval between doses>