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Math Help - problem solving in differential equations

  1. #1
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    problem solving in differential equations

    This one has been bugging me. I cant seem to figure it out. can anyone help..??



    A tumor may be regarded as a population of multiplying cells. It is found empirically that the birth rate of the cells in a tumor decreases exponentially with time so that β( t) = β0e-αt ( where α and β0 are positive constants).
    And hence
    dP/dt = β0e-αt P
    P(0) = P0

    1.Solve this initial value problem for P(t) = P0exp ( 0/α(1- e-αt)

    Observe that P(t) approaches the finite limiting population P0exp(0/α) as t approaches infinity.
    2.Suppose that at time t=0 there are P0 = 106 cells and that P(t) is then increasing at the rate of 3 x105 cells per month. After 6 months the tumor has doubled (in size and in number of cells). Solve numerically for α , and then find the limiting population of the tumor.
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  2. #2
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    Quote Originally Posted by mathprincess24 View Post
    This one has been bugging me. I cant seem to figure it out. can anyone help..??



    A tumor may be regarded as a population of multiplying cells. It is found empirically that the birth rate of the cells in a tumor decreases exponentially with time so that β( t) = β0e-αt ( where α and β0 are positive constants).
    And hence
    dP/dt = β0e-αt P
    P(0) = P0

    1.Solve this initial value problem for P(t) = P0exp ( 0/α(1- e-αt)

    Observe that P(t) approaches the finite limiting population P0exp(0/α) as t approaches infinity.
    2.Suppose that at time t=0 there are P0 = 106 cells and that P(t) is then increasing at the rate of 3 x105 cells per month. After 6 months the tumor has doubled (in size and in number of cells). Solve numerically for α , and then find the limiting population of the tumor.
    What exactly is your difficulty? T start with, do you know how to solve a separable differential equation such at this?
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  3. #3
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    the letters just make it confusing
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  4. #4
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    am i solving the equation written under question 1 or am i solving the one given in the introductory information. i just dont even know where to start with this. can you help me a bit more?
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  5. #5
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    this is still troubling me. can anyone help me with this?
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