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. a) Find the relative growth rate. I know how to do everything but the last part
k = 3ln(2) hr−1
(b) Find an expression for the number of cells after t hours.
P(t) =
40e3tln(2)
(c) Find the number of cells after 5 hours.
1310720 cells
(d) Find the rate of growth after 5 hours. (Round your answer to the nearest integer.)
2725566 cells/h
(e) When will the population reach a million cells? It has to be in the ln(?)/ln(?) form.
ln(20,000)ln(5)​