The given problem describes how light energy spreads out as it moves away from a light source, with the area of coverage increasing as a function of distance. The area covered at different distances from the lightbulb is determined by the size of the grid at those distances.

We are told that at 1 yard from the bulb, the energy passes through an area of 1 square unit, and as the distance increases, the grid size forms a square that grows proportionally to the distance.

Pattern Explanation:

The number of square units in each grid corresponds to the square of the distance from the lightbulb, because the grid is expanding both horizontally and vertically.

• At 1 yard: $1^2 = 1$ square unit
• At 2 yards: $2^2 = 4$ square units
• At 3 yards: $3^2 = 9$ square units
• At 4 yards: $4^2 = 16$ square units

Answers:

• 2 yards away: $2^2 = 4$ square units
• 3 yards away: $3^2 = 9$ square units
• 4 yards away: $4^2 = 16$ square units

Summary:

• 2 yards away: $4$ square units
• 3 yards away: $9$ square units
• 4 yards away: $16$ square units

Would you like more details or have any questions?

Here are 5 related questions to deepen understanding:

1. How does the area change if the distance is doubled?
2. How would the intensity of light change as the area increases?
3. Can this pattern be applied to sound waves or other forms of energy?
4. What would the area be at 5 yards from the light source?
5. How would the area change if the shape of the grid wasn't square but rectangular?

Tip: Light intensity decreases as the area of coverage increases, since the same amount of energy is spread over a larger area. This follows the inverse square law.