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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