5. After going for a swim in a pond on uncle Leroy\'s farm, you realize one of t

Question

5. After going for a swim in a pond on uncle Leroy's farm, you realize one of the snozzlewhompin scratches you received the day before is rather nicely infected, oozing a yellowish-green pus and smelling somewhat similar to Trader Joe's White Cheddar Popcorn. Since the closest medical facility is a day and half from uncle Leroy's farm, you decide to see what the microbe it is that has infected your scratch by examining a sample under the microscope. Upon examination, you discover that you are infected with a rare amoeboid critter that divides via mitosis every 60 minutes. Assuming a single amoeba initiated the infection, estimate the population size considering that it has been 24 hours since your swim.

a) Alarmed by the geometric growth you calculated above, you a do a bit of research on the ol' interwebs (I know, hard to believe uncle Leroy has access, right!) and discover that the amoeba infecting you reaches a lethal concentration at approximately 1.0 x 1010 cells, and has an intrinsic rate of increase (rm) of 0.7 per hour. Given this information, how long (in hours) will it be from the initial infection until the amoeboid population reaches a fatal concentration? Think you'll survive?

b) There are 4 biological processes that contribute to growth (or reduction) in population density. In the models of population growth you used to answer 5 and 5a, which two of these processes have you accounted for? What are the two you have you ignored?

Explanation / Answer

5) The number of organisms in a medium after n number of generations is calculated by the formula,

2number of generations x initial count

Here, the organism divides every 60 minutes. Therefore, in 24 hours we have 24 generations.

Single organism initiated the infection.

The estimated population size = 2 24 x 1

= 16,777,216

a) The lethal concentration of the organism is approximately 1 x 1010

The time taken to reach lethal concentration is given by the formula,

2number of generations x initial count = 1 x 1010

2x x 1 = 1 x 1010

2x = 1010

log 2x = log 10 10

x log 2 = 10 log 10

x = (10 log 10) / log 2

x = (10 x 1) / 0.3010

x = 33.22

Therefore, the organism has to multiply in 33.22 generations to reach lethal dose

1 generation equals 1 hour.

33.22 generations equals 33 hours and 13 minutes.

The closest medical facility is 36 hours away.

So, it will be difficult to survive this infection.

b) The biological process that contibute to growth or reduction in population density are,

In the example cited above, we have considered competition within the population and waste accumulation and have ignored predation and disease and parasites.

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