*Myoglobin* and

*hemoglobin* are oxygen carrying molecules in the human body. Hemoglobin is found inside red blood cells, which flow from the lungs to the muscles through the bloodstream. Myoglobin is found in muscle cells. The function

calculates the fraction of myoglobin saturated with oxygen at a given pressure

*p* torrs. For example, at a pressure of

1 torr,
M(1) = 0.5,

which means half of the myoglobin (i.e., 50%) is oxygen saturated. (Note: More precisely, you need to use something called the "partial pressure," but the distinction is not important for this problem.) Likewise, the function

Y =

H(

p) =

p^{2.8} |

26^{2.8} + p^{2.8} |

calculates the fraction of hemoglobin saturated with oxygen at a given pressure

*p*.

(a) The graphs of

*M*(

*p*) and

*H*(

*p*) are given below on the domain

0 ≤ p ≤ 100;

which is which?

(b) If the pressure in the lungs is 100 torrs, what is the level of oxygen saturation of the hemoglobin in the lungs? (Round your answer to three decimal places.)

(c) The pressure in an active muscle is

10 torrs. What is the level of oxygen saturation of myoglobin in an active muscle? (Round your answer to three decimal places.)

What is the level of hemoglobin saturation in an active muscle? (Round your answer to three decimal places.)

(d) Define the efficiency of oxygen transport at a given pressure

*p* to be

M(p) − H(p).

What is the oxygen transport efficiency at

10 torrs? (Round your answer to three decimal places.)

At

30 torrs? (Round your answer to three decimal places.)

At

60 torrs? (Round your answer to three decimal places.)

Sketch the graph of

M(p) − H(p).

Are there conditions under which transport efficiency is maximized? Explain.