Question

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.

Answer 1

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

Answer 2

Can you please explain how you solved this equation? Im confused.