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Math Help - Population Growth problem

  1. #1
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    Population Growth problem

    The rate of growth of dP/dt of a population of bacteria is proportional to the square root of t, where P is the population size and t is the time in days.

    dP/dt= k*sqrt t

    The initial size of the population is 500. After 1 day, the population has grown to 600. Estimate the population after 7 days.
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Hello,
     <br />
\frac{dp}{dt}=k \sqrt{t}<br />
    Integrate both sides

     <br />
p=\frac{2k*\sqrt{t^3}}{3}+c<br />

    for t=0 p=500
    hence c=500

    for t=1
    p=2k/3+c=600
    thus
    k=150
    -----------------------------------------------------
    Try yourself now else see below
    so
    Now for 7 days
    Population
     <br />
=\frac{300*\sqrt{7^3}}{3}+500<br />
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  3. #3
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    Can you explain what k is in the problem? Is it just a variable for an unknown constant?
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  4. #4
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    Quote Originally Posted by yeloc View Post
    Can you explain what k is in the problem? Is it just a variable for an unknown constant?
    k represents a constant whose value you have to find (actually I should use past tense since the value has been found).
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  5. #5
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    Thank you adarsh and mr fantastic for the responses.
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