Posted by **Sinha** on Monday, June 25, 2012 at 3:42am.

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.

- Maths - Ant Colony -
**Bosnian**, Monday, June 25, 2012 at 4:28am
Interpolation polynomial for first set :

( x ^ 5 - 100 x ^ 4 + 4375 x ^ 3 - 65000 x ^ 2 + 827500 x + 2250000 ) / 37500

Interpolation polynomial for second set :

8 x + 400

( x ^ 5 - 100 x ^ 4 + 4375 x ^ 3 - 65000 x ^ 2 + 827500 x + 2250000 ) / 37500 = 8 x + 400

Real solution :

x = 25.91833

- Maths - Ant Colony -
**Sinha**, Tuesday, June 26, 2012 at 6:53am
Can you please explain how you solved this equation? Im confused.

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