Medicine and mathematics

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Medicine and Mathematic

Investigation By - Akash Singh

Introduction

As you may have realized from the title, this investigation in sincerely based on the use of medicine and mathematics, we will be investigating how penicillin reacts in the body, and how its concentration decreases in the bloodstream. Penicillin was named the miracle drug, as its properties and against fighting bacterial infections were very effective. Penicillin was discovered in 1929 through Sir Alexander Fleming.

Medicine and Mathematics

Part A

Well if you look at the table give above you will see that the amount of insulin administrated is 10,00 micro units. So “half of the original dosage (10,00 Micro Units) , will be (5,00 Micro Units).

Looking at the table, it takes 15 minutes after the dosage of insulin is at half of the original dosage so at 5,00 Micro units.

Question 2.

In the equation y=10(0.95)x, 10 represent the units of insulin that started off in the bloodstream, and when the units of insulin reduce each minute, that value is multiplied with 0.95 to get the units of insulin after every minute. So basically (0.95) represent the fraction of the original dose.  The x is the amount of time /m at which the certain amount of insulin is active in the blood stream.

Question 3

From the table and the previous question we know to our knowledge that it takes 15 minutes for the amount of insulin to be reduced to half of the original. Therefore we can substitute the ^x to be 15. This will then be: “0.95¹ x 10 = 4.63” “5 when rounded up”. Though the following answers shows us that the formula given above is not 100% accurate as the answers should equal 5; as that is the half life of the insulin.

As we know the half-life of Insulin, we can use the the function y=10(0.95)x to show how long it takes to reach its half-life. We substitute y=s - Where y is representing the half-life.  And make x the subject of the formula

5=10*(0.95)x 

…Making x the subject we get

x= Log0.950.5

x=13.5134073

x=13.5 (3s.f.)

Part B

Q4.

From the info provided in the investigation, you understand that every hour after the administration of the original dose, only 60% of insulin will remain active. This basically is means that every successive hour, the next value will be 60% of the value before it.  The insulin was administrated at 07:00, and amount of penicillin active at that moment was 300.00. So, at 08:00 only 60% of 300.00 will still be active meaning: 180.00

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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 ...

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