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Math Help - Two bacterial colonies

  1. #1
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    Two bacterial colonies

    Two bacteria colonies are cultivated in a laboratory. The first colony has a doubling time of 2 hours and the second a doubling time of 3 hours. Initially, the first colony contains 1000 bacteria and the second colony 3,000 bacteria. At what time t will sizes of the colonies be equal?

    We never learned this in class, and he expects us to know it for the next one. I have no idea what to do here. :S
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    What kind of function doubles when you increase t by a certain amount each time?
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    By researching a bit, I have come to the conclusion that this is an exponential growth function. We never learned this, lol.
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    You are correct. Can you figure out exactly which functions will fit your conditions? (You'll need two separate functions here, one for each colony.)
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    Hmm, nope, I have no clue.
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    Ok. Well, let's just take the first colony. You know that its initial population is 1000, and it has a doubling time of 2 hours. I would posit a function of the form

    P(t)=K\,n^{kt}.

    What happens when you plug in t = 0? What does that say about the value of K?
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    It basically says that when t = 0, the answer will be K. I'm guessing k has a direct relationship with P
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    Well, yes, it does have a direct relationship. When t = 0, your function returns K. But you know the population when t = 0, don't you?
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    The population would be 0 would it not? P(0) = 0.
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    No, no. This is the population when you start the clock. The initial population. What is that?
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  11. #11
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    1,000 or 3,000, depending on the colony.
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    Right. Well, we were looking at just the first colony, as per Post # 6. So, what does this tell you about the equation in Post # 6 for the first colony?
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    When t = 0, the population will be 1,000.
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    So K is... what?
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    K is the new population after a certain amount of time.
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