Hill's equation for the oxygen saturation of blood states that the level of oxygen saturation (fraction of hemoglobin molecules that are bound to oxygen) in blood can be represented by the following function, where P is the oxygen concentration around the blood (P20) and n is a parameter that varies between different species. Answer parts (a) through (f) below. pn f(P) = p +30 (a) Assume the n = 1. Show that f(P) is an increasing function of P and that f(P)-1 as P→∞o. Choose the correct answer below. О А. О в. O C. If n = 1, f(P) = If n = 1, f(P) = If n = 1, f(P) = P P+30 P P+30 P P+30 and f'(P) = 30 (P+30)² and f'(P) = - and f'(P) = - . The function f(P) is an increasing function since the slope of the curve y=f(P) is always positive. As P→∞o, lim f(P) = lim P P→∞ P+30 P→∞ 30 (P+30)² 60 (P+30)³ 1 = lim = 1. P001 P The function f(P) is an increasing function since the slope of the curve y=f(P) is always negative. As P→∞o, lim f(P) = lim P→∞ P→∞0 P+30 The function f(P) is an increasing function since the slope of the curve y=f(P) is always negative. As P→∞o, lim f(P) = lim P→∞ = lim P→∞ P P→∞ P+30 P→∞ 1 = 1. 1 = lim = 1.
Hill's equation for the oxygen saturation of blood states that the level of oxygen saturation (fraction of hemoglobin molecules that are bound to oxygen) in blood can be represented by the following function, where P is the oxygen concentration around the blood (P20) and n is a parameter that varies between different species. Answer parts (a) through (f) below. pn f(P) = p +30 (a) Assume the n = 1. Show that f(P) is an increasing function of P and that f(P)-1 as P→∞o. Choose the correct answer below. О А. О в. O C. If n = 1, f(P) = If n = 1, f(P) = If n = 1, f(P) = P P+30 P P+30 P P+30 and f'(P) = 30 (P+30)² and f'(P) = - and f'(P) = - . The function f(P) is an increasing function since the slope of the curve y=f(P) is always positive. As P→∞o, lim f(P) = lim P P→∞ P+30 P→∞ 30 (P+30)² 60 (P+30)³ 1 = lim = 1. P001 P The function f(P) is an increasing function since the slope of the curve y=f(P) is always negative. As P→∞o, lim f(P) = lim P→∞ P→∞0 P+30 The function f(P) is an increasing function since the slope of the curve y=f(P) is always negative. As P→∞o, lim f(P) = lim P→∞ = lim P→∞ P P→∞ P+30 P→∞ 1 = 1. 1 = lim = 1.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Hill's equation for the oxygen saturation of blood states that the level of oxygen saturation (fraction of hemoglobin molecules that are bound to oxygen) in blood can be represented by the
following function, where P is the oxygen concentration around the blood (P≥0) and n is a parameter that varies between different species. Answer parts (a) through (f) below.
pn
f(P) =
p +30
(a) Assume the n=1. Show that f(P) is an increasing function of P and that f(P)-1 as P→∞o. Choose the correct answer below.
OA.
O B.
O C.
O D.
If n = 1, f(P) =
If n = 1, f(P) =
If n = 1, f(P) =
If n = 1, f(P) =
P
and f'(P) =
P + 30
P
P + 30
P
P + 30
30
(P+30)²
and f'(P) = -
and f'(P) = -
P
and f'(P) =
P + 30
30
(P+30)²
CI
The function f(P) is an increasing function since the slope of the curve y=f(P) is always positive. As P→∞o, lim f(P) = lim
P→∞ P→∞0
60
(P+30)³
60
(P+30)³
P
P+30 P→∞
= lim
P
P+30 P→∞ 1
P→∞ P+30
= lim
The function f(P) is an increasing function since the slope of the curve y=f(P) is always negative. As P→∞o, lim f(P) = lim
P→∞0 P→∞0
The function f(P) is an increasing function since the slope of the curve y=f(P) is always negative. As P→∞o, lim f(P) = lim
P→∞
1
P
1
= lim=1
P→∞ P+30 P→∞
P
P→∞0 P+30 P001
-= lim
The function f(P) is an increasing function since the slope of the curve y=f(P) is always positive. As P→∞o, lim f(P) = lim
P→∞
-=1.
= 1.
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