7. Suppose the surface area of the shell of an egg is directly proportional to t

Question

7. Suppose the surface area of the shell of an egg is directly proportional to the 2/3
power of the mass of the egg. An average chicken egg has a mass of 60 grams, and it has a surface area of 28cm^2.

a. What are the independent and dependent variables? What is the domain of the problem situation? Range?

b. Determine a function to represent the relationship between the surface are of the shell of an egg and the mass of the egg.

c. What would be the surface area of an ostrich egg that has a mass of 1,600 grams?

d. what would be the mass of a turtle egg that has a surface area of 15 cm^2

Explanation / Answer

The independent variable is m (mass of the egg) and the dependent variable is the surface area. Theoretically, the mass could range anywhere from 0 to infinity. Since mass is your independent variable, this is your domain (0,) (you cant have a negaive mass so the range starts at 0). This is also your range since s (surface area) is proportional to 2/3 the power of the mass.

Since the surface area is proportional to the 2/3 power of the mass, the surface area (s) as a function of mass (m) is

s(m) = km2/3 where k is some constant; use the given values to solve for k

28=k*602/3 so k = 28/602/3 = 1.827 so your function is s(m) = 1.827*m2/3

To answer part c simply plug 1600 into the equation to get 249.92 cm2

To answer part d, set the equation equal to 15 and solve for m to get 23.53 g (15 = 1.827*m2/3)

Related Questions

Navigate

• Browse (All)
• Browse 7
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.