Hi doma,
Have you been attending online maths class?
"1. The doubling time for a certain bacteria is one minute. A biologist has put a single
bacterium in a jar at 11:00 am. With the doubling time listed, she knows the jar will be full
at noon.
a. How many bacteria are in the jar at 11:07?
Let y be the number of bacteria at a given time.
At time 0 (11:00), we have 1 bacterium, so
the model is
y = ebt
At 11:01, there are 2 bacteria, so
2 = eb ) b = ln 2 ) y = eln(2)t
Hence, there are y = eln(2)7 = 27 = 128 bacteria at 11:07.
b. How many bacteria are in the jar at 11:30?
y = eln(2)30 = 230 = a big number
c. At what time will the jar be half full? Explain your reasoning.
The jar will be half full at 11:59, because in the next minute, the population of bacteria
will double and at 12:00 the jar will be full.
d. Some of the biologist's friends are going to lunch at 11:45. The biologist wants to go
but knows her bacteria jar will be full before she can make it back. She decides to split the
bacteria between 2 jars of the same size in order to buy her more time for lunch. Is this a good idea? Explain.
Not a good idea, it only gains her 1 minute!"
http://pages.uoregon.edu/dmoseley/m106su09/Math106Su09Worksheet2Solns.pdf
Cactus maths:
What happens to the rate of growth when the jar is full?
No more bacteria can fit in the jar, so the population levels off: the bacterial death rate will necessarily equal the bacterial birth rate.
I guess the earth isn't quite full yet as we keep adding people.
Air is approximately infinite relative to its use by human beings. That's because we have a means to employ it (ie a respiratory system) which costs nothing; but when you go underwater, you'd pay for its use.
In the environment we inhabit, electricity is a scarce resource because in order to use it, we have to purchase access to a system that makes it available for our use.
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