Question

Infections seldom start with a single bacterium. Suppose that you cut yourself on a rusty nail that puts 25

bacteria cells into the wound. Suppose a to that those bacteria divide in two after every quarter of an hour.
a. Make and record a guess of how many bacteria you think would be present in the cut after 8 hours
(32 quarter-hours) if the infection continues to spread as predicted. (Assume that your body does
not fight off the infection and you do not apply medication.) Then answer the following questions to
check your ability to estimate the rate of exponential growth.

Answer 1

Answer: There would be 12,000 bacteria 8 hours after the initial infection.

Step-by-step explanation: You start with 25 cells and if they divide every 15 minutes, 25 multiplied by 15 gets you 375 cells every quarter of an hour. Then if you multiply that by the 32 quarter hours, you get 12,000 cells. To check that you can also multiply 25 by 15, still 375, then 375 by 4 for each quarter of the hour, then that gets you 1,500 cells every hour. If you multiply that by 8 for the 8 hours they have time to divide, you still get 12,000 cells.

I hope this helps!