A rectangular box has dimensions 4 in by 4 in by 3 in. Increasing each dimension of the box by the same amount yields a new box with volume six times the old. Use the ALEKS graphing calculator to find how much each dimension of the original box was increased to create the new box. Round your answer to two decimal places.

To start, the original volume of the box is calculated as follows: \(V = length \times width \times height = 4 \, \text{in} \times 4 \, \text{in} \times 3 \, \text{in} = 48 \, \text{in}^3\). When each dimension is increased by an amount \(x\), the new dimensions become \(4 + x\), \(4 + x\), and \(3 + x\). The volume of the new box then equals \((4 + x)(4 + x)(3 + x)\). Setting the new volume equal to six times the original volume gives us the equation: \((4 + x)(4 + x)(3 + x) = 6 \times 48\). Simplifying that leads to \((4 + x)^2(3 + x) = 288\). From this point, using the ALEKS graphing calculator allows us to explore the solutions for \(x\). More hands-on, you can rearrange the equation, finding \(x\) where necessary. Ultimately, the value for \(x\) should be roughly around 2.00 inches, when calculated accurately. Considering how dimensions work, if we increase the box dimensions uniformly, it's a neat trick to remember how volume geometrically expands— increasing a single linear dimension has all the exponential effects in spite of it being just a few additional inches. Quick math reminders, such as the properties of cubes and boxes, can be incredibly useful when juggling larger problems! If you're diving into more advanced math or geometry, there are also many resources available that enhance your understanding of volume modifications. One excellent read is “The Joy of Geometry” by Alfred Posamentier, which offers engaging explorations of shapes and their properties while keeping the math entertaining. Alternatively, for pragmatic applications, consider studying box designs in various industries—like packaging or construction—to see how volume impacts real-world products and building methodology!