The illustration shows that the light energy that passes through the first unit of area, 1 yard away from the bulb, spreads out as it travels away from the source.

A glowing lightbulb gives off a beam of energy. As the beam travels away from the lightbulb, it expands and passes through four square grids of unequal size at four distances. At a distance of 1 yd, the beam passes through the first grid, which is made up of a single square, and labeled "1 square unit." At a distance of 2 yd, the beam passes through the second grid, which is made up of two rows of two squares. At a distance of 3 yd, the beam passes through the third grid, which is made up of three rows of three squares. At a distance of 4 yd, the beam passes the fourth grid, which is made up of four rows of four squares.
How much area does that energy cover 2 yards, 3 yards, and 4 yards from the bulb? Express each answer using exponents.
2 yards away	
  square units
3 yards away	
  square units
4 yards away	
  square units

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.

The illustration shows that the light energy that passes through the first unit of area, 1 yard away from the bulb, spreads out as it travels away from the source. A glowing lightbulb gives off a beam of energy. As the beam travels away from the lightbulb, it expands and passes through four square grids of unequal size at four distances. At a distance of 1 yd, the beam passes through the first grid, which is made up of a single square, and labeled '1 square unit.' At a distance of 2 yd, the beam passes through the second grid, which is made up of two rows of two squares. At a distance of 3 yd, the beam passes through the third grid, which is made up of three rows of three squares. At a distance of 4 yd, the beam passes the fourth grid, which is made up of four rows of four squares. How much area does that energy cover 2 yards, 3 yards, and 4 yards from the bulb? Express each answer using exponents.

Discover how to calculate the area of light coverage at increasing distances from a light source. Learn about how energy expands in a square grid pattern as it travels away from the bulb. Explore the formula area = distance^2 with answers for distances of 2, 3, and 4 yards from the source. Suitable for Grades 6-8.

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