HONORS ALG. 2
10 – 4 Applications of Common Logs ___________________________
Relative Intensity of Sound
The relative intensity, R, of a sound in decibels (dB) is given by the function
I
I = sound intensity, I 0  the threshold of hearing
R  10 log , where
I0
threshold of hearing = 0 decibels
1. The relative intensity of a loud siren is about 1013 times as loud as the threshold of hearing, I 0
. Find the relative intensity, R, of the loud siren.
2. The sound of a leaf blower is about 1010.5 times the intensity of the threshold of hearing, I 0 .
Find the relative intensity, R, of this leaf blower in decibels.
3. Suppose that the relative intensity, R, of a rock band is about 115 decibels. Compare the
intensity of this band with that of the threshold of hearing, I 0 .
4. A small jet engine produces a sound whose intensity is one billion times as loud as the
threshold of hearing. What is the relative intensity of the engine’s sound in decibels?
pH level of a substance:
In chemistry, the pH of a substance is defined as
pH   log H  , where H  is the hydrogen ion concentration in moles per liter.
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An acidic solution has a pH value in the range 0 < pH < 7.
An alkaline solution has a pH value in the range 7 < pH < 14.
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5. For hydrochloric acid, H  is about 5  10 2 moles per liter. Find the pH for this strong acid to
the nearest tenth.
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6. For milk of magnesia, H  is about 3.2  10 11 moles per liter. Find the pH of milk of
magnesia to the nearest tenth.
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7. Find the pH of orange juice: H   3.16  10 4 moles per liter.
Magnitude of earthquakes
On the Richter scale, the magnitude, M, of an earthquake depends on the amount of energy, E,
released by the earthquake as follows:
2
E
M  log 11.8
3
10
The amount of energy E, measured in ergs, is based on the amount of ground motion recorded
by a seismograph at a known distance from the epicenter of the quake.
The logarithmic function for the Richter scale assigns very large numbers for the amount of
energy, E, to numbers that range from 1 to 9. A rating of 2 on the Richter scale indicates the
smallest tremor that can be detected. Destructive earthquakes are those rated greater than 6
on the Richter scale.
-------------------------------------------------------------------------------------8. In 1976, an earthquake that released about 8  1019 ergs of energy occurred in San Salvador,
El Salvador. Find the magnitude, M, of this earthquake to the nearest tenth.
9. One of the strongest earthquakes in recent history occurred in Mexico City in 1985. The
amount of energy released by this earthquake was approximately 8.91 10 23 ergs. Find the
magnitude, M, of this earthquake to the nearest tenth.
10. In 1989, an earthquake that measured 7.1 on the Richter scale occurred in San Francisco,
CA. Find the amount of energy, E, released by this earthquake.
11. On May 10, 1997, a light earthquake with a magnitude of 4.7 struck the Calaveras Fault 10
miles east of San Jose, California. Find the amount of energy, E, released by this earthquake.
Compound Interest
nt
 r
A  P 1   ,
 n
where P = the principal,
r = interest rate as a decimal,
n = # of times interest is compounded per year,
t = time in years
------------------------------------------------------------------------------------12. $25,000 is invested at an interest rate of 5% for 30 years. Find the value of the investment
after 30 years, if the interest is compounded:
a) annually
b) quarterly
c) monthly
13. $8,000 is invested at 6% interest, compounded annually. Determine how much the
investment is worth after:
a) 10 years
b) 15 years
c) 25 years
14. How long does it take an investment of $12,000 invested at a rate of 5%, compounded
annually, to double in value? (Use the Rule of 72 to get an approximation, then use the
compound interest formula to get the exact answer)
15. How long does it take an investment of $20,000 invested at a rate of 4%, compounded
annually, to be worth $30,000?