Question

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?

Answer 1

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]