Question

Given a doubling time of 2,395 minutes, how long will it take a culture to grow from 97 cells per mL, to 43,252 cells per mL?

• Report your answer in minutes, rounded to 2 decimal places.
• Do not use exponential notation.

Answer 1

We have

Nt = N0 * eGrowth Rate * Time

Doubling time is the time taken for the population to double in size, such that:

In(2) Doubling Time = = Growth Rate

=> 2395 min = 0.693 Growth Rate

0.693 => Growth Rate == 2395 min = 0.000289 cells/min

So,

43,252 cells/mL = 97 cells/mL * e0.000289 * t​​​​​​

=> 445.8969 = e0.000289 * t

=> ln(445.8969) = 0.000289 * t

=> t * 0.000289 = 6.100087

=> t = 6.100087/0.000289 = 6854.03

​The grozth fron 97 cells per mL to 43,252 cells per mL will take 6854.03 minutes.