Posted by **Ajay** on Wednesday, June 27, 2012 at 4:22am.

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) -
**Steve**, Wednesday, June 27, 2012 at 10:26am
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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