Suppose a scientist is watching a video that models the growth of bacteria. He is taking screen shots of the video after every second of “video time,” with each second of video time correlating to 20 minutes of “real time.” In the video, each bacteria cell splits into two cells with each passing second, as seen in the images from the video. In these screenshots, t is the video time in seconds.
T = 0, T = 1 , T = 2, T = 3
Use the information from the images to complete the table. Then determine the total number of bacteria after the first hour (60 minutes).
Time (seconds of video), t 0 1 2 3
Number of Bacteria, B(t)
The bacteria count at the end of the first hour is
.
Time (seconds of video), t 0 1 2 3
Number of Bacteria, B(t) 1 2 4 8
To determine the total number of bacteria after the first hour (60 minutes), we need to find the value of B(180), where 180 represents the video time in seconds.
Based on the pattern observed in the table, it can be observed that the number of bacteria doubles with each passing second. Therefore, the general formula would be B(t) = 2^t.
So, B(180) = 2^180 = 1,152,921,504,606,846,976
Therefore, the total number of bacteria after the first hour is 1,152,921,504,606,846,976.