Exponential Population Growth Model

A simple population growth model is derived, solved and plotted to answer the following question:
A certain bacteria exhibits exponential growth.The bacteria contains 100 cells initially and 739 cells after" 20" minutes. Determine the number of cells present at any time.

The governing differential equation is first found. A general solution is then found using the method of seperable equations. A particular solution is found by applying the given conditions, and the solution is finally confirmed by plotting it out over the corresponding slope field.