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    Table shows the number of bacteria present in a particular sample for the first 5 minutes


    Time Bacteria present
    0 2
    1 4
    2 8
    3 16
    4 32
    5 64

    Note: The 0,1,2,3,4,5 is time and other figures are bacteria. I couldn't make a table properly.

    Use Algebra to extend this model for the growth of bacteria colonies with following conditions:
    The relationship between the number of bacteria and the size of the colony and ;Different rates of replication

    Hi guys i am stuck at this question as i dont know in what way i should be extending the model. Please share your insights about how to tackle this question.


    F(t) = 2^t+1 or 2(2)^t
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    (Original post by Jyashi)
    Table shows the number of bacteria present in a particular sample for the first 5 minutes


    Time Bacteria present
    0 2
    1 4
    2 8
    3 16
    4 32
    5 64

    Note: The 0,1,2,3,4,5 is time and other figures are bacteria. I couldn't make a table properly.

    Use Algebra to extend this model for the growth of bacteria colonies with following conditions:
    The relationship between the number of bacteria and the size of the colony and ;Different rates of replication

    Hi guys i am stuck at this question as i dont know in what way i should be extending the model. Please share your insights about how to tackle this question.
    Well, you first want to express \text{number of bacteria} = f(time)

    You can see that (calling B the number of bacteria) B = f(t), where f is some function of t you need to find. It's pretty easy, exponential.
    Spoiler:
    Show
    B = 2^{t+1}
    .
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    (Original post by Zacken)
    Well, you first want to express \text{number of bacteria} = f(time)

    You can see that (calling B the number of bacteria) B = f(t), where f is some function of t you need to find. It's pretty easy, exponential.
    Spoiler:
    Show
    B = 2^{t+1}
    .
    Thank you for your answer. already knew the function is (2)^t+1 as i also know it can also be 2(2)^t

    But i dont know what to do after this.
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    (Original post by Jyashi)
    Thank you for your answer. already knew the function is (2)^t+1 as i also know it can also be 2(2)^t

    But i dont know what to do after this.
    As it stands your question is missing information, why don't you post a picture of your question so we can better help you? (THE FULL QUESTION)

    Also, 2^{t+1} = 2^{t} \cdot 2 = 2 \cdot 2^{t} by the law of indices.
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    (Original post by Zacken)
    As it stands your question is missing information, why don't you post a picture of your question so we can better help you? (THE FULL QUESTION)

    Also, 2^{t+1} = 2^{t} \cdot 2 = 2 \cdot 2^{t} by the law of indices.
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    (Original post by Jyashi)
    Table shows the number of bacteria present in a particular sample for the first 5 minutes


    Time Bacteria present
    0 2
    1 4
    2 8
    3 16
    4 32
    5 64

    Note: The 0,1,2,3,4,5 is time and other figures are bacteria. I couldn't make a table properly.

    Use Algebra to extend this model for the growth of bacteria colonies with following conditions:
    The relationship between the number of bacteria and the size of the colony and ;Different rates of replication

    Hi guys i am stuck at this question as i dont know in what way i should be extending the model. Please share your insights about how to tackle this question.


    F(t) = 2^t+1 or 2(2)^t
    So you have a series  2, 4, 8, 16, 32, 64, ... You should see that this is clearly a geometric progression with first term and common ratio 2. The amount of bacteria present at any time t is given by  B(t) = 2\times2^{t} = 2^{t+1}

    The rate of growth is given by the rate of change of bacteria with respect to time  \displaystyle\frac{dB}{dt} = 2^{t+1}ln(2) .

    If we started with a different number at time = 0 then we could adapt the model by letting the first term a be generic, so  B(x) = a2^{t} . This would mean  \displaystyle\frac{dB}{dt} = 2^{t}ln(2^a)
    I think this is what the question is getting at however I'm not 100% sure.
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    (Original post by Louisb19)
    So you have a series  2, 4, 8, 16, 32, 64, ... You should see that this is clearly a geometric progression with first term and common ratio 2. The amount of bacteria present at any time t is given by  B(t) = 2\times2^{t} = 2^{t+1}

    The rate of growth is given by the rate of change of bacteria with respect to time  \displaystyle\frac{dB}{dt} = 2^{t+1}ln(2) .

    If we started with a different number at time = 0 then we could adapt the model by letting the first term a be generic, so  B(x) = a2^{t} . This would mean  \displaystyle\frac{dB}{dt} = 2^{t}ln(2^a)
    I think this is what the question is getting at however I'm not 100% sure.
    That would be because it isn't a question per se, more like a project that involves real data researcg, etc...
 
 
 
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