General Physics Foundation Course – Problem Solving Exercises 5
Exponential and Logarithmic Functions
1. Evaluate the exponential function for the given x-values.
a) A: g(0)=1; g(4)=81
b) a: g(-2)=0.01; g(3)=1000
c) ; a: h(2)=9/4; h(-3)=8/27
d) a: j(-1)=4; j(5)=1/1024
2. Use the calculator to evaluate the exponential function for the given x-values. Round to the nearest
hundredth.
a) A: g(3.2)=9.19
b) a: h(pi)=0.11
c)
a: g(2)=7.39, g(-2)=-0.14, g(0)=1, g(2.2)=9.03
3. For photo-chromatic eyeglass lenses their transparency changes depending on the intensity of the UV light.
The intensity of UV rays is measured using a scale called UV index. On this scale, a value near 0 indicates
a low UV intensity and a value near 10 indicates a high UV intensity. For a particular type of the photochromatic
lenses their transparency P depends on the current UV index x as:
.
a) Find the transparency of the lenses, to the nearest tenth of a percent,when they are exposed to light rays
with a UV index of 3.5.
a: P=0.692 <=> 69.2%
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b) What is the UV index of light rays that cause these photo-chromatic lenses to have a transparency of
45%? Round to the nearest tenth.
A: use log(0.45)=x*log(0.9) → x=log(0.45)/log(0.9)=7.6
4. A sample of 40.0 g of tritium, 3
1H, is produced. What will be the mass of the tritium remaining after 61.5
years? (3
1H half life is 12.3 years)
a: 40*(1/2)5
........ m=1.25 g
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5. The half-life of plutonium 336
94Pu is 2.9 years. How long does it take before 1 g of 336
94Pu out of the original
amount of 8 g ?
a: (1/8)=(1/2)n-half-lifes
n=3 => t=thalf-life * 3; t=8.7 years
6. Write each equation in its exponential form:
a) a:
b) a:
c) a:
d) a:
e) a:
f) a:
7. Write each equation in its logarithmic form:
a) a:
b) a:
c) a:
d) a:
e) a:
f) a:
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8. Evaluate, do not use calculator:
a) a: 2
b) a: -5
c) a: 1
d) a: -2
e) a: 6
f) a: 2*log_5(125)=6
g) a: 1/5*log_3(9)= 2/5
h) a: 2/3
9. Write each expression as a single logarithm with a coefficient 1:
a) a:
b) a:
c) a:
10. Use the change-of-base formula to approximate the logarithm accurate to the nearest tenthousandth.
a) A: 1.5395
b) a: 0.7901
c) a: -0.1215
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11. What is decibel level (given by dB(I)=10 log(I/I0) ) of a fire-alarm with sound intensity I=I0*1014
, a handdrill
with sound intensity I=I0*1010
, a typical conversation with sound intensity I=I0*106
?
A: 140, 100, and 60
12. What multiple of the base intensity is the intensity of a moderate rainfall with the decibel level of 50 and a
quiet room with decibel level of 40.
a: *I0, *I0
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