The count in a bacteria culture was 700 after 20 minutes and 1000 after 40 minutes. What was the initial size of the culture?
2 Answers
490 microorganisms.
Explanation:
I will assume exponential growth for bacteria. This means that we can model the growth with an exponential function:
where
Sub the two known values into the function to get two equations:
Divide (2) by (1) to find
Take the natural log of both sides to isolate
Now that we have the growth constant,
Initial culture size was
Explanation:
The growth can be considered as a geometric progression with the same rate of growth after each interval of
The rate of growth can be determined by
In terms of the size of the initial population
This means:
So if we reverse the process we just divide by
Remember that