Question
A culture of bacteria has an initial population of 3900 bacteria and
doubles every 2 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 9 hours, to the nearest whole number?
Answer Attempt out of 2

To solve this, we can plug the values into the formula . Given that , hours, and hours, we first need to calculate how many times the bacteria have doubled in 9 hours. This is done by , which means the bacteria double 4 times fully and then halve a bit on the fifth time.

Next, compute:
.
Calculating gives approximately 22.63. Finally, multiplying this by 3900 gives us roughly 87,500. So, the population after 9 hours is about 87,500 bacteria.

But don’t forget to round that to the nearest whole number: the final answer is 87,500 bacteria.

For some history, the study of bacteria and their growth has roots in the late 17th century, when Antonie van Leeuwenhoek first observed microorganisms through his handmade microscope. This sparked a scientific revolution, leading to germ theory and advances in microbiology. Understanding bacterial growth has become crucial, not only for biology but also for medicine and biotechnology!

When calculating bacterial growth, it’s easy to lose track of the doubling intervals. A common mistake is neglecting to correctly determine how many complete doubling times fit into the total time. Always double-check your and values to avoid underestimating or overestimating the final population. Remember, bacteria don’t just multiply—they party hard (and fast)!