College Algebra 9th txtbk

SECTION 5–4 Logarithmic Models 371
8. SOUND If the intensity of a sound from one source is 10,000
times that of another, how much more is the decibel level of the
louder sound than the quieter one?
9. EARTHQUAKES One of the strongest recorded earthquakes to
date was in Colombia in 1906, with an energy release of
1.99 10 17 joules. What was its magnitude on the Richter scale?
Compute the answer to one decimal place.
10. EARTHQUAKES Anchorage, Alaska, had a major earthquake in
1964 that released 7.08 10 16 joules of energy. What was its magnitude
on the Richter scale? Compute the answer to one decimal
place.
11. EARTHQUAKES The 1933 Long Beach, California, earthquake
had a Richter scale reading of 6.3, and the 1964 Anchorage, Alaska,
earthquake had a Richter scale reading of 8.3. How many times
more powerful was the Anchorage earthquake than the Long Beach
earthquake?
12. EARTHQUAKES Generally, an earthquake requires a magnitude
of over 5.6 on the Richter scale to inflict serious damage. How
many times more powerful than this was the great 1906 Colombia
earthquake, which registered a magnitude of 8.6 on the Richter
scale?
13. EXPLOSIVE ENERGY The atomic bomb dropped on Nagasaki,
Japan, on August 9, 1945, released about 1.34 10 14 joules of
energy. What would be the magnitude of an earthquake that released
that much energy?
14. EXPLOSIVE ENERGY The largest and most powerful nuclear
weapon ever detonated was tested by the Soviet Union on October 30,
1961, on an island in the Arctic Sea. The blast was so powerful there
were reports of windows breaking in Finland, over 700 miles away.
The detonation released about 2.1 10 17 joules of energy. What
would be the magnitude of an earthquake that released that much
energy?
15. ASTRONOMY A moderate-size solar flare observed on the sun on
July 9, 1996, released enough energy to power the United States for
almost 23,000 years at 2001 consumption levels, 2.38 10 21 joules.
What would be the magnitude of an earthquake that released that
much energy?
16. CONSTRUCTION The energy released by a typical construction
site explosion is about 7.94 10 5 joules. What would be the
magnitude of an earthquake that released that much energy?
17. SPACE VEHICLES A new solid-fuel rocket has a weight ratio
W tW b 19.8 and an exhaust velocity c 2.57 kilometers per
second. What is its velocity at burnout? Compute the answer to two
decimal places.
18. SPACE VEHICLES A liquid-fuel rocket has a weight ratio
W tW b 6.2 and an exhaust velocity c 5.2 kilometers per second.
What is its velocity at burnout? Compute the answer to two
decimal places.
19. CHEMISTRY The hydrogen ion concentration of a substance is
related to its acidity and basicity. Because hydrogen ion concentrations
vary over a very wide range, logarithms are used to create a
compressed pH scale, which is defined as follows:
pH log [H ]
where [H ] is the hydrogen ion concentration, in moles per liter.
Pure water has a pH of 7, which means it is neutral. Substances with
a pH less than 7 are acidic, and those with a pH greater than 7 are
basic. Compute the pH of each substance listed, given the indicated
hydrogen ion concentration. Also, indicate whether each substance
is acidic or basic. Compute answers to one decimal place.
(A) Seawater, 4.63 10 9
(B) Vinegar, 9.32 10 4
20. CHEMISTRY Refer to Problem 19. Compute the pH of each
substance below, given the indicated hydrogen ion concentration.
Also, indicate whether it is acidic or basic. Compute answers to one
decimal place.
(A) Milk, 2.83 10 7
(B) Garden mulch, 3.78 10 6
21. ECOLOGY Refer to Problem 19. Many lakes in Canada and the
United States will no longer sustain some forms of wildlife because
of the increase in acidity of the water from acid rain and
snow caused by sulfur dioxide emissions from industry. If the pH
of a sample of rainwater is 5.2, what is its hydrogen ion concentration
in moles per liter? Compute the answer to two significant
digits.
22. ECOLOGY Refer to Problem 19. If normal rainwater has a pH of
5.7, what is its hydrogen ion concentration in moles per liter? Compute
the answer to two significant digits.
23. ASTRONOMY The brightness of stars is expressed in terms of
magnitudes on a numerical scale that increases as the brightness
decreases. The magnitude m is given by the formula
m 6 2.5 log L L 0
where L is the light flux of the star and is the light flux of the
dimmest stars visible to the naked eye.
(A) What is the magnitude of the dimmest stars visible to the
naked eye?
(B) How many times brighter is a star of magnitude 1 than a star of
magnitude 6?
24. ASTRONOMY An optical instrument is required to observe stars
beyond the sixth magnitude, the limit of ordinary vision. However,
even optical instruments have their limitations. The limiting magnitude
L of any optical telescope with lens diameter D, in inches, is
given by
L 8.8 5.1 log D
(A) Find the limiting magnitude for a homemade 6-inch reflecting
telescope.
(B) Find the diameter of a lens that would have a limiting magnitude
of 20.6.
Compute answers to three significant digits.
Problems 25 and 26 require a graphing calculator or a computer
program that can calculate a logarithmic regression model for a
given data set.
25. INTERNET ACCESS Table 4 on page 372 shows the percentage
of Americans that had access to the Internet either at home or at
work between 2000 and 2006. Let x represent years since 1995.
L 0