A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 71 cells. (a) Find the relative growth rate. (Assume t is measured in hours.) k =

Step-by-step explanation:

Given that a common inhabitant of human intestines is the bacterium Escherichia coli.

A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes.

Initial population = 71 cells

Doubles in 1/3 of an hour

, where t is the no of hours.

Rate of growth = derivative of P

=

since we know that the two functions are equal, f (x) = g

(x), therefore when we equate the two equations the result should be similar to

3x = x – 4:

a. f(x) = 3x, g(x) = x – 4

equating the two functions:

3x = x – 4             (correct)

so we now got our answer (a)