21, 2017 Due November MATH 141-PROJECT 4 I. How to Manage Population Growt We kn

Question

21, 2017 Due November MATH 141-PROJECT 4 I. How to Manage Population Growt We know that population grows exponentially, Lets see what this mea splits every min ns for a type of bacteria that Spits every minute. Suppose that at 12:00 noon a single bac bacterium and its descendants are all happy bacteria-doomsday single bacterium colonizes a discarded food can. The but they fear the time when the can is completely full of 1. How many bacteria arein the can at 12:05? At 12.107 full of bacteria at 1:00 P.M. At what time was the can only half full of bacteria at The can is completely bacteria? 2. can is exactly half full, the president of the bacteria colony reassures his constituents -after all, there is as much room left in the can as has been used in 3. When the that doomsday is far away the entire previous history of the colony. 4. Is the president correct? 5. How much time is left before doomsday? 6. When the can is a quarter full, how much time is left till doomsday?

Explanation / Answer

bacteria splits every minute: after one minute, 1 bacteria to 2 bacteria

after 2 minutes, 2 bacteria to 2*2 = 4 bacteria.

Hence after 5 minutes: 25 bacteria = 32 bacteria at 12:05

At 12:10: after 10 minutes bacteria = 210 = 1024 bacteria

2.

since the bacteria is doubling every minute, if completely full at 1PM, it was half full just one minute ago

12:59 PM it was half full.

3&4. The president is wrong since when half full, the time was 12:59 PM, and when completely full it was 1PM. Hence only 1 minute difference.

5. Only 1 minute left till doomsday

6.

Quarter full = 1/2*Half full.

hence it takes 1 minute to go from quarter full to half full. At 12:58PM it was quarter full. Hence, 2 minutes till dooms day.

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