Unformatted text preview: from maintaining
a healthy ﬁsh tank to regulating the pH levels in blood. Our next example shows how the pH in
a buﬀer solution is a little more complicated than the pH we ﬁrst encountered in Exercise 6c in
Section 6.1.
Example 6.5.7. Blood is a buﬀer solution. When carbon dioxide is absorbed into the bloodstream
it produces carbonic acid and lowers the pH. The body compensates by producing bicarbonate, a
weak base to partially neutralize the acid. The equation18 which models blood pH in this situation
00
is pH = 6.1 + log 8x , where x is the partial pressure of carbon dioxide in arterial blood, measured
in torr. Find the partial pressure of carbon dioxide in arterial blood if the pH is 7.4.
00
00
Solution. We set pH = 7.4 and get 7.4 = 6.1 + log 8x , or log 8x = 1.3. Solving, we ﬁnd
800
x = 101.3 ≈ 40.09. Hence, the partial pressure of carbon dioxide in the blood is about 40 torr. Another place logarithms are used is in data analysis. Suppose, for instance, we wish to model
the spread of inuenza A (H1N1), the socalled ‘Swine Flu’. Below is data taken from the World
Health Organization (WHO) where t represents the number of days since April 28, 2009, and N
represents the number of conﬁrmed cases of H1N1 virus worldwide.
t
N 1
2
3
4
5
6
7
8
9
10
11
12
13
148 257 367 658 898 1085 1490 1893 2371 2500 3440 4379 4694
t
N 14
5251 15
16
17
18
19
20
5728 6497 7520 8451 8480 8829 Making a scatter plot of the data treating t as the independent variable and N as th...
View
Full Document
 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

Click to edit the document details