Ant Colony (Maths)
posted by Ajay .
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.

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 + (800570)/5 t = 600 + (640600)/5 t at t = .789
So, at somewhere around t = 25.789 weeks the ants and food are balanced