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Math Help - Growth Formula

  1. #1
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    Growth Formula

    A colony of 10 000 roughly circular organisms grows in culture, each with density 0.4 g/cm2 and radius r cm. The energy consumption of the colony is given by

    E = 250*[ m / (1000+m) ]

    m is its total mass. Find E as a function of the radius r, and determine what
    happends to E as r gets large. What does this tell you about this colony?

    I know that mass = density*radius, so

    E = 250[ (0.4*pi*r^2) / (1000 + 0.4*pi*r^2) ]

    What happens to E as r gets larger?
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  2. #2
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    Re: Growth Formula

    Quote Originally Posted by Manni View Post
    A colony of 10 000 roughly circular organisms grows in culture, each with density 0.4 g/cm2 and radius r cm. The energy consumption of the colony is given by

    E = 250*[ m / (1000+m) ]

    m is its total mass. Find E as a function of the radius r, and determine what
    happends to E as r gets large. What does this tell you about this colony?

    I know that mass = density*radius, so

    E = 250[ (0.4*pi*r^2) / (1000 + 0.4*pi*r^2) ]

    What happens to E as r gets larger?
    Judging by your units: mass = density * area [although you did do the correct calculation].

    Are you allowed to use L'hopital's rule?

    Essentially you want to find \lim_{r \to \infty} E(r)
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  3. #3
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    Re: Growth Formula

    What is L'hopital's rule? And how would I evaluate this limit? It seems a little tricky
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