Suppose the surface area of the shell of an egg is directly proportianal to the 2.3 power of the mass of the egg. An average chicken egg has a mass of 60 g, and it has a surfgace area of 28cm^2.
Since the surface area is directly proportional to the `2/3` rd power of the mass of the egg, we have `A=km^(2/3)` where A is the surface area, k a constant of proportionality, and m the mass.
For a chicken egg we have `28=k(60)^(2/3)` . Solving for `k` we get:
(a) The independent variable is the mass of the given egg. The dependent variable is the egg's surface area.
The domain is m>0 and the range is A>1.82694.
The function is `A=1.82694m^(2/3)` where A is the surface area in square cm and m is the mass in g.
(b) Given an egg with mass 1600g:
`A=1.82694(1600)^(2/3)~~249.92` sq cm
So an ostrich egg has approximately 250 sq cm of surface area.