The doubling function (y = y base0 2^(1/D)) can be used to model exponential growth when the doubling time is D. The bacterium Escherichia coli has a doubling period of 0.32 h. A culture of E. coli starts with 100 bacteria.

Question

a) Determine the equation for the number of bacteria, y, in x hours.
b) Graph your equation
c) Graph the inverse
d) Determine the equation of the inverse. What does this equation represent?
e) How many hours will it take for there to be 450 bacteria in the culture? Explain your strategy.

Answer 1

equation:

y = 100 (2)^(t/3.2)

..
..

to get 450 bacteria
450 = 100 (2)^(x/3.2)
4.5 = 2^(x/3.2)
take log of both sides and use log rules
(x/3.2)log 2 = log 4.5
x/3.2 = log 4.5/log2
x = 6.944 hrs. or appr 7 hours