Question: Consider the following statement from Michael Crichton's book Andromeda Strain (Dell, N.Y., 1969 , p. 247)

"The mathematics of uncontrolled growth are frightening. A single cell of the bacterium E. coli would, under ideal circumstances, divide every twenty minutes. That is not particularly disturbing until you think about it, but the fact is that bacteria multiply [exponentially]: one becomes two, two become four, four become eight, and so on. In this way it can be shown that in a single day, one cell of E. coli could produce a supercolony equal in size and weight to the entire planet Earth."

Assume that Crichton's ideal circumstances hold and determine whether his statement is correct under the realistic assumptions that:

- the mass of an E. coli bacterium is approximately \(10^{-12}\) grams

- the mass of the earth is approximately \(5.9763 \times 10^{24}\) kilograms

- the volume of an \(\mathrm{E}\). coli bacterium is approximately \(0.5 \mu \mathrm{m}^{3}\)

- the volume of the earth is \(1.08 \times 10^{12} \mathrm{~km}\)

Support your answer using calculations.

[Hint: Find a function of the form \(N=N_{0} a^{k t}\) to describe the number of bacteria present at any given time.

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