# 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