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248 Chapter 3 Exponential and Logarithmic Functions
45.
10 log 10 I
I 0
46.
10 log 10 I
I 0
10
10
I
I 0
1010
I
I 0
I I 0 10
10
I I 0 1010
% decrease I 010 8.8 I 0 10 7.2
I 0 10 8.8 100
97.5%
% decrease I 0 109.3 I 0 10 8.0
I 0 10 9.3 100 95%
47. pH log 10 H log 10 2.3 10 5 4.64
48.
5.8 log 10 H
10 5.8 H
H 1.58 10 6 moles per liter
49.
pH log 10 H
pH log 10 H
10 pH H
Hydrogen ion concentration of grape
Hydrogen ion concentration of milk of magnesia
103.5
10.5
107
10
50.
pH 1 log 10 H
pH 1 log 10 H
10 pH1 H
10 pH1 H
10 pH 10 H
The hydrogen ion concentration is increased by a
factor of 10.
51. (a)
P 120,000, r 0.075, M 839.06
u M M Pr
12 1 r
12 12t
839.06 839.06 7501 0.00625 12t
v 839.06 7501.00625 12t
850
(b) In the early years, the majority of the monthly
payment goes toward interest. The interest and
principle are equal when t 20.729 21 years.
(c) P 120,000, r 0.075, M 966.71
u 966.71 966.71 7501.00625 12t
v 966.71 7501.00625 12t
u
v
1500
52.
(a)
0
0
0.075t
u 120,0001
1
1 0.07512 1 12t
120,000
30
0
0
u
v
u v when t 10.73 years.
(b) From the graph, when u 120,000, t 21.2 years.
Yes, a mortgage of approximately 37.6 years will
result in about $240,000 of interest.
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