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## Homework Statement

A colony of bacteria is grown under ideal conditions in a laboratory so that the population increases exponentially with time. At the end of 3 hours there are 10,000 bacteria. At the end of 5 hours there are 40,000. How many bacteria were present initially?

## Homework Equations

## The Attempt at a Solution

I have the following two equations setup:

10,000 = Ne^(3k)

40,000 = Ne^(5k)

I understand that this looks like a differential equation where I have to make them equal and solve for k (growth rate) and N (initial population) but I'm not quite sure how.