A culture of bacteria has an initial population of 750 bacteria and doubles
every 9 hours. Using the formula , where is the
population after hours, is the initial population, is the time in
hours and is the doubling time, what is the population of bacteria in the
culture after 4 hours, to the nearest whole number?

To find the population of bacteria after 4 hours, we can use the formula provided:

Here,
(initial population),
(time in hours),
and (doubling time).

Plugging in these values:

Calculating gives approximately 0.4444.

So we calculate:

Now, multiplying out:

Rounding to the nearest whole number, the population after 4 hours is approximately 1061 bacteria.

You can also think of this exponential growth as a tiny, bustling city of bacteria, popping up more residents every chance they get, just like how a flourishing community doubles with new inhabitants! It’s fascinating to visualize such growth in a microscopic culture.

In real-world applications, understanding bacterial growth helps in fields like medicine, food preservation, and environmental science, where controlling bacterial populations can be crucial. For example, strategies used in fermentation leverage this growth pattern to produce delicious foods and beverages. Who knew bacteria could have such a tasty outcome?