Initial concentration is $10$ mg$/$L$.$ The environmental carry capacity is $100$ mg$/$L and the value of r $($growth rate$)$ is $2/$day$.$ Plot the concentration vs$.$ time using the analytic solution to the logistic model and the Euler solution to the logistic model. Use $6-$hour time steps and plot for $5$ days. Use units of days on the x axis. Print out this graph, and explain why there is a slight difference in the curves.

Harvest at the optimal harvest rate from the beginning of the culture and plot the concentration with the Euler method with harvest. Plot the analytic solution for growth without harvest for $10$ days. Explain the difference in the concentrations.