Suppose Celine wants to choose a box that maximizes the amount of cereal it can hold.Volume of Box 1: 3x5Volume of Box 2: 4x5 – x4If Celine decides the width of the cereal boxes will be greater than 1, which box will hold more cereal? Explain.

Answer:

Box 2 will hold more cereal. Since the width x is greater than 1, we can compare the volumes by subtracting Box 1's volume from Box 2's: (4x^5 - x^4) - 3x^5 = x^5 - x^4. For any value of x > 1, x^5 is greater than x^4, making the difference positive. Therefore, Box 2 has a larger volume than Box 1 for all x > 1.