Bacterial Colony(infected!)

Algebra Level 3

On day 1 at midnight, a scientist keeps some bacteria in a jar. The population of bacteria grows exponentially, doubling every day. After 30 complete days, the jar is completely filled with bacteria.

When was three-eighths of the jar was filled?

12 p.m. of 28th day 2 p.m. of the 28th day 2 a.m. of the 28th day 2 p.m. of the 29th day 12 p.m. of 29th day

1 solution

Fabrício Oishi Grigolin
Sep 30, 2015

The growth function in the n-th day is given by:

$f(n) = P_{0}2^{n}$

Where $P_{0}$ is the initial population of bacteria. If the final amount is $P_{f}$ :

$f(30) = P_{f} = P_{0}2^{30}$

So $P_{0} = \frac{P_{f}}{2^{30}}$

So for $f(n) = \frac{3}{8}{P_{f}} = P_{0}2^{n} = \frac{P_{f}}{2^{30}}2^{n}$

$n = log_{2} (3.{2^{27}}) = 27 + \log_2 3 = 28.585 days = 28 days 14 hours$

Wouldn't that make it 2 p.m. on the 29th day? You have days 1 through 28, and then 14 hours of day 29.

Denton Young - 4 years, 3 months ago

Bacterial Colony(infected!)

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