Math Problem Statement

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

Solution

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Math Problem Analysis

Mathematical Concepts

Algebra
Geometry
Exponentiation

Formulas

Area = distance^2

Theorems

Inverse Square Law

Suitable Grade Level

Grades 6-8