Case Study: you are working in a lab that is trying to engineer a new version of the Cas9 protein. You design a way to synthesize the protein in a bacteria "bio-factory" and decide a batch reactor is suitable for this task. Sadly, it is the end of Winter Quarter and time for a holiday break in which you cannot be in the lab for 10 days. Q1: Using the equation below, and the provided parameters, solve for the initial condition (i. e. cell concentration) that is needed to obtain exactly 80% of the carrying capacity after 10 days. Please show all your work! Chosen System: Bacteria and Food in a tank with linear K(c) function N(t) NoB No + (B – N.)e-" Parameters: Alpha=3 (unitless) Cor 9 mg/L R=0.05 L/(mg* days)
Q2: In your own words, justify the use of this equation. Specifically, do you expect the equation to be most accurate before or after the population reaches the carrying capacity (plateau)?