A common inhabitant of human intestines is the bacterium Escherichia coli, named after the German pediatrician Theodor Escherich, who identified it in 1885. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 40 cells.
Find the Growth Rate.

Question

A common inhabitant of human intestines is the bacterium Escherichia coli, named after the German pediatrician Theodor Escherich, who identified it in 1885. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 40 cells.
Find the Growth Rate.

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dumbcow · Answer

Population doubles every 20 min, so when t =20, population = 40*2
exponential function will look like this:
$$\large 40 (2^{\frac{t}{20}})$$
The growth rate comes from the following exponential form
$$(1+r)^t$$
where "1+r" is the base of the exponential function
set equal the bases and solve for r
$$\rightarrow 1+r = 2^{\frac{1}{20}}$$
$$r = 2^{\frac{1}{20}} - 1$$