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Math Help - Pop'n Model equation

  1. #1
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    Pop'n Model equation

    Given that the population of a certain fish species increases according to the model below:

    \frac{dP}{dt}=0.3\left(1-\frac{P}{200}\right)\left(\frac{P}{50}-1\right)P

    1.) Determine the values for P where the pop'n is at equilibrium.

    2.) Use Euler's Method to approximate the time it would take for an initial pop'n of 58,000 to grow to 175,000.

    ------

    So, for #1 we just set dP/dt = 0, and solve for P

    0= 0.3\left(1-\frac{P}{200}\right)\left(\frac{P}{50}-1\right)P

    P = 0 or P = 50 or P = 200.

    Not sure for #2!
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  2. #2
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    Quote Originally Posted by fifthrapiers View Post
    Given that the population of a certain fish species increases according to the model below:

    \frac{dP}{dt}=0.3\left(1-\frac{P}{200}\right)\left(\frac{P}{50}-1\right)P

    1.) Determine the values for P where the pop'n is at equilibrium.

    2.) Use Euler's Method to approximate the time it would take for an initial pop'n of 58,000 to grow to 175,000.

    ------

    So, for #1 we just set dP/dt = 0, and solve for P

    0= 0.3\left(1-\frac{P}{200}\right)\left(\frac{P}{50}-1\right)P

    P = 0 or P = 50 or P = 200.

    Not sure for #2!
    You start with P(0)=58000, then use the stepping formula:

    <br />
P(t+\delta t) = P(t)+\delta t P'(t)=P(t)+\delta t \left[ 0.3\left(1-\frac{P(t)}{200}\right)\left(\frac{P(t)}{50}-1\right)P(t) \right]

    to step forward untill P\approx175000, best done in a spreadsheet.

    RonL
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