A student is trying to determine the concentration of bacteria in a sample using

Question

A student is trying to determine the concentration of bacteria in a sample using direct microscopic count. The student puts 0.01 mL of the sample on a slide in a circle with a radius of 1 cm and counts the bacteria in 5 microscopic views. The results are as follows: {60, 57,40,45,48}. The student uses a stage micrometer and measures the microscopic view as diameter of 0.2 mm. What is the concentration of the sample in bacteria per mL?

Answer is: 50,000,000 bactria/mL

I need a step-by-step explanation on how to obtain the answer since I have no idea how to get it. Thank you!

Explanation / Answer

The student puts 0.01 mL of the sample on a slide in a circle with a radius of 1 cm and counts the bacteria in 5 microscopic views. The results are as follows: 60, 57, 40, 45, 48.

So, the average count of bacteria is (60 + 57 + 40 + 45 + 48) = 250 / 5 = 50 in 0.01 ml sample.

So, in 1 ml sample, the count of bacteria is 50 X 102.

For the circle, the radius is 1 cm = 10 mm

Area (A) = ?r2 = ? (10)2 = 100?

For the circle of microscopic view, the diameter is 0.2 mm.

So, the radius is 0.1 mm.

Area (A) = ?r2 = ? (0.1)2 = 0.01?

So, the circle on the slide is (100? / 0.01?) = 1 X 104 times bigger than the circle of microscopic view.

Therefore, the concentration of the sample in bacteria per mL is = (50 X 102) X (1 X 104) = 50 X 106 = 50,000,000 bactria/mL.

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