Two mathematically inclined ants are racing to a piece of candy. Ant 1 starts at point M and reaches for a candy at point Q. Ant 2 starts at point A and reaches for a candy at point M. The diagram is not drawn to scale. Ant 1 follows a semicircular path with diameter MN = NO = OP = PQ. Ant 2 follows a square path where AB = BC = CD = AD. MN = AD = X.

1. Express the distance traveled by ant 1 as f(X)

2. Express the distance traveled by ant 2 as g(X)

3. Express the difference between f(X) - g(X) as a function of X

4. Which ant chose the more efficient scenic route?

5. What would have been the most efficient path?

6. A science question- Why do you think ants often don't travel on a straight path?

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