Question

Working in lab, you've set up an E. coli culture for a critical experiment where you need to grow the cells @27 degrees C until they reach a cell density of exactly 6 x 10^8 cells/ml & then you'll need to rapidly harvest them to perform a critical bioassay. Unfortunately, you used a very old stationary culture to inoculate your culture & so the cells spent a lot of time in lag phase before they entered into exponential growth. (continued)

Answer 1

Consequently, it's now 8:30pm & you're so hungry that you're considering eating a smelly taco that you put in your backpack this morning & then forgot to put in the refrigerator at lab. It suddenly occurs to you that there's a sandwich place that's open till 9pm & you can get there on your bike before closing time & make it back to the lab by 9:30 pm.

You really want a sandwich but if your cells reach a density of > 6 x 10^8 cells/ml before you get back they cannot be used for the bioassay & you'll not only have to start all over again tomorrow but will also have to endure snarky comments from your lab supervisor.

When you measured the cell density at 8:30, it was 2 x 10^8 cells/ml but, unfortunately, you don't know the generation time of this strain of E. coli at 27 degrees C (you usually grow the cells at 37 degrees C & you know that the generation time at that temperature is 30 min). But then you remember your beloved professor yammering on about something called the Ahrennius equation..

A) Do you have time to go get that sandwich?
B) What is your best estimate for the time the cells will be ready for harvest? Show you work.