Two transparent spheres have the same radius.[br]Inside each sphere, a colored ball changes size in some simple fashion.[br][br]"Simple Fashion" means some size parameter changes at a constant rate.[br]However, what is "simple" for Green may not be simple for Red.

Animate the size changes (time t varies between 0.00 and 1.00).[br][list=1][*]Try to identify what aspect of the Red ball changes at a constant rate;[br][/*][*]identify which aspect of the Green ball changes at a constant rate.[br][/*][*]Suppose radius of the Red ball is a power function of t, i.e., some constant k times a power p of t: [math]radius_{Red}=f\left(t\right)=k\cdot t^p[/math]. Find a plausible value for p.[/*][*]Make a similar conjecture for radius of the Green ball.[br][/*][*]Does either of these balls change in a fashion which is similar to a spherical balloon being inflated at a constant rate by an air compressor (e.g., volume increases at the rate of 200 cubic-inches per minute)?[br][/*][/list]