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March 25, 2017

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A colony of ants is growing so that the total number of ants present, A, after a
number of weeks, t, is shown in the table.
t 5 10 15 20 25 30
A 140 200 280 400 570 800
The food supply available is such that it can feed A ants at any given time, t (weeks),according to the table below.
t 5 10 15 20 25 30
A 440 480 520 560 600 640
At what point in time are the ant population and food supply balanced?
Fully justify your response.

  • Ant Colony (Maths) - ,

    Assume the graphs are linear between given points. Probably not true, but it's a good first approximation.

    A(t) = F(t) for some 25 < t < 30

    570 + (800-570)/5 t = 600 + (640-600)/5 t at t = .789

    So, at somewhere around t = 25.789 weeks the ants and food are balanced

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