Final answer:
The volume of the cube as a function of the number of minutes elapsed, denoted as m, is V(m) = (4 + 6m)^3. This represents the volume after m minutes when the edge length increases at a rate of 6 feet per minute from an initial length of 4 feet.
Step-by-step explanation:
To express the volume of a cube as a function of m, the number of minutes elapsed, we first need to understand that the volume V of a cube is calculated by cubing the edge length L.
Initially, the edge length is 4 feet. Since the edge length is increasing at a rate of 6 feet per minute, after m minutes, the edge length will be L = 4 + 6m feet.
Therefore, the volume of the cube after m minutes can be expressed as:
V(m) = (L)^3 = (4 + 6m)^3
By expanding this expression, we can find the volume as a function of time:
V(m) = 64 + 288m + 432m² + 216m³
This equation allows us to calculate the volume of the cube at any given time m minutes after the increase begins.