A bacterial culture in a petri dish grows at an exponential rate. The petri dish has an area of 256
, and the bacterial culture stops growing when it covers this area. The area in that the
bacteria cover each day is given by the function . What is a reasonable domain for this
function?
A
B
C
(

Let’s dive into this bacterial growth fun! The function describes an exponential growth function where the area covered doubles each day. Since the maximum area of the petri dish is 256 , we need to stop growing once it reaches this limit.

To find the reasonable domain for this function, we consider when reaches 256. Setting , we find that . Thus, must be non-negative, leading us to conclude that the reasonable domain is actually . This corresponds to option D.

Additionally, remember that exponential functions grow rapidly, so it’s essential to monitor the growth rate to ensure we don’t overflow our petri dish!

For further exploration, don’t forget to check out the ‘Logarithmic Functions’ that can help you better understand the relationship between exponential growth and its inverse. Plus, if you’re interested in the applications of exponential growth, think about how the human population proliferates or how viruses spread - it’s always fascinating to see math play a role in the real world!