Thomas Calculus 13th [Solutions]

520 Chapter 7 Integrals and Transcendental Functions
(b)
0.00771 t
(0.00771)(140)
T Ts T0 Ts e Ts y Ts 70 Ts
T e
1.0794
y 70e
23.79 C
0.00771t
(0.00771) t
(c)
0 0.00771t
T T
0
s T0 Ts e Ts 10 Ts 70 Ts Ts
e 10 70e
ln 1 0.00771t 1 1
7 0 t 0
ln 252.39 252.39 20 232 minutes from now the
0.00771 7
silver will be 10°C above room temperature
(5700)
45. From Example 4, the half-life of carbon-14 is 5700 1 k
yr c ln 2
2 0 c0e k 0.0001216
5700
0.0001216t
0.0001216t
ln(0.445)
c c0e (0.445) c0 c0e t
6659 years
0.0001216
s
46. From Exercise 45, k 0.0001216 for carbon-14.
(a)
(b)
(c)
c c0e 0.0001216t
(0.17) c0 c0e 0.0001216t
t 14,571.44 years 12,571 BC
(0.18) c0 c0e 0.0001216t
t 14,101.41 years 12,101 BC
(0.16) c0 c0e 0.0001216t
t 15,069.98 years 13,070 BC
0.0001216t
47. From Exercise 45, k 0.0001216 for carbon-14 y y0e . When t 5000
0.0001216(5000)
y
y y0e 0.5444y 0 0.5444 approximately 54.44% remains
y
48. From Exercise 45, k 0.0001216 for carbon-14. Thus,
t
ln(0.995)
0.0001216
41 years old
0
0.0001216t
0.0001216t
c c0e (0.995) c0 c0e
49.
(ln 2/5730) t
ln 2 5730ln(0.15)
e 0.15 t ln(0.15) t
15,683 years
5730 ln 2
(ln 2/5730)(500)
50. (a) e 0.94131, or about 94%.
(b) Well assume that the error could be 1% of the original amount. If the percentage of carbon-14 remaining
5730ln(0.93131)
were 0.93131, the Ice Maidens actual age would be
588 years.
ln 2
Copyright
2014 Pearson Education, Inc.