The volume of a sphere is directly proportional to the cube of its diameter. The volume of a sphere with a diameter of 12 inches is 288π in3. In terms of π, what is the constant of proportionality? To the nearest tenth, what is the volume of a sphere with a diameter of 3 inches?

The volume of a microbial culture is observed to increase according to the formula V (cm^3) = e^t where t is time in seconds

a) calculate the expression for V (in^3) in terms of t (h)

b) both the exponential function and its argument must be dimensionless. the given equation seems to violate both of these rules, and yet the equation is valid. explain this paradox. [hint: observe the result of part a]