Please explain how to do all the parts to this question These seven problems are
ID: 91742 • Letter: P
Question
Please explain how to do all the parts to this question
These seven problems are for you to practice applying the exponential, geometric, and logistic population growth equations presented in class. You do not need to turn this in but if you have trouble doing any of these please stop by or ask me after class. 1. You have a large beaker continuously supplied with nutrients containing bacterial strain LB. The published data for strain LB indicates that they have a population doubling time of 15 minutes when grown under ideal conditions as you have provided in this beaker.
(a) Assuming these bacteria are growing continuously, calculate r for the LB population.
(b) If the population is now 5.4 million, how big will it be in 7 minutes?
(c) How big will the population be 10 minutes after this (i.e., 17 minutes from now)?
Explanation / Answer
Answer:
(a) tdouble = ln (2) / r
Therefore, r = ln (2) / t
t = 15 minutes, and so r = ln (2) / 50 = 0.0462 bacteria/(bacteria x minutes)
(b) No = population size = 5.4 million
t = 7 minutes
r = 0.0462 (from question above)
Nt = No ert
Nt = (54,00,000) e(0.0462)(7)
Nt/54,00,000 = e0.3234
ln (Nt/54,00,000) = ln (e0.3234)
ln Nt - ln (54,00,000) = 0.3234
ln Nt = 15.825
Nt = 7459507.84 = 7.45950784 = 7.459 million
(c) No = population size = 7.459 million
t = 10 minutes
r = 0.0462 (from question above)
Nt = No ert
Nt = (7459507) e(0.0462)(10)
Nt/7459507 = e0.462
ln (Nt/7459507) = ln (e0.462)
ln Nt - ln (7459507) = 0.462
ln Nt = 16.287
Nt = 11840068.7886 = 11.840068 = 11.84 million