Scientists wanted to know how many individual amoeba cells go into a slug. To figure this out, they estimated the volume of an individual amoeba and the volume of a slug, then did arithmetic to find the number of amoeba in a slug.

In 1953, two scientists, Bonner and Frascella, estimated the diameter of a single Dictyostelium discoideum to be 8 micrometers. They also measured the volume of a Dictyostelium discoideum slug. With these measurements, they estimated there are about 100,000 amoeba in a single slug.

In 1998, Bonner returned to the problem and used new methods to estimate the diameter of a single amoeba. This time, he found 4 micrometers for the average diameter. Bonner did not change his estimate of the volume of a slug between 1953 and 1998. He also didn't change his assumptions about the shape of amoeba, just the overall scale.

Bonner used his updated diameter measurement to re-estimate the number of amoeba in a single slug. What was his new estimate?

(You should enter a number as your answer. To answer this problem, try thinking about the dimensions of the quantities involved; you won't need to use any geometric volume formulas.)

 Oct 5, 2023

The diameter of the amoeba is given in micrometers, which is the same as microliters (μL). The volume of a sphere is proportional to the cube of its radius, so the volume of an amoeba is proportional to the cube of its diameter.

If the diameter of the amoeba is halved, the volume is reduced by a factor of 23=8. Therefore, the new estimate of the number of amoeba in a slug is 100,000/8=12,500​.

 Oct 6, 2023

The amoeba were actually found to be smaller, so there should be more of them, not less

LachrymoseMath  Oct 6, 2023

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