This table illustrates the power of exponential population growth. Populations c

Question

This table illustrates the power of exponential population growth. Populations can grow exponentially and achieve very large sizes quite quickly. For example, some bacteria ca duplicate every hour. If you started with 1 bacterium, how many hours would it take to reach 8 million bacteria? Answer: In the example above, the rate at which rice grains or bacteria reproduce is very fast, they double at every step (or generation). Most organisms do not reproduce that fast, but they can still grow exponentially

Explanation / Answer

Ans. Bacterial growth kinetics is given by-

ln (N2/ N1) = k (t2-t1)                  - equation 1

where, t2 = final time,         t1= initial time (0 hrs),

N2= population at t2 (final population),

N1= population at t1 (initial population),

k = specific growth rate = ln 2/ g

g = generation time

Given,

Generation time, g = 1.0 hr

            N1 = 1

            N2 = 8 million = 8.0 x 106

            Take initial time, t1 = 0

Now,

            Specific growth rate, k = ln 2 / g = 0.693 / (1 hr) = 0.693 hr-1

Putting the values in equation 1-

            ln (8.0 x 106 / 1) = 0.693 hr-1 (t2 - 0)

            Or, 15.895 = 0.693 hr-1 (t2)

            Or, t2 = 15.895 / (0.693 hr-1)

            Hence, t2 = 22.94 hr

Therefore, required time = 22.94 hr

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