Aptos High School Global Health Odyssey
Health Professionals Use Math for Problem Solving


Medical Lab Technician 6.

Infections vary in strength; that is, how much of the virus or bacteria it takes to make you sick. Some diseases are fatal at 100 microbes per ml, some take 1,000,000! It is important to find out the concentration of pathogens by diluting blood until we can count the particles easily in a small sample.

In order to determine the count, or potency, of a certain disease in a sample of blood, a medical lab technician must find the smallest concentration of blood that will react with a serum containing antibodies to that pathogen. The technician performs a serial dilution by consecutively halving a blood sample to see the smallest concentration that will produce a reaction.

This is important in determining the dose of medicine required to combat the disease, and the amount of time since the person has been exposed. In an epidemic this is very important information.

1st step: 1 ml blood = 100% blood = 1.00
2nd step: 1/2 ml blood + 1/2 ml water = 1/2 blood = 50% = .50 blood
3rd step: 1/2 ml of step 2 product (1/2 blood) + 1/2 ml water
            = 1/4 blood =25% = .25 blood .

She continues to dilute the blood in this manner and finds that the 10th dilution is the last one that will react with the serum.

What is the concentration of the 10th dilution? Express your answer as a fraction, decimal, and %.

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