# 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. a. What are the independent and dependent variables? what is the domain of the problem and what is the range? Determin a function to represent the relationsihp between the surface area of the shell of an egg and the mass of an egg. What would be the surface are aof an ostrich egg tha thas a mas of 1,600 g.

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:

`k=28/(60^(2/3))~~1.82694`

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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:

`k=28/(60^(2/3))~~1.82694`

(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.

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