Analysis
PRACTICE
Date
Write as the su4i or difference of logarithms with no exponents.
1.
log 1000y 5
3
2.
log
107/68
4-
Write as a single logarithm.
3.
8logc-1-51ogd
5.
loga M
Use the formula log o M = lo b to find lo
ga
to the nearest thousandth.
"--
4.
log5 1 — log5 25
7.
31+3x = 5 1+x
.y
Solve.
6.
6 = 2'
Dafi 3 3
(Li
V-)
8.
3e 2x-1 _____. 12
9.
0,410
1.11,y
1og5 2 — log5 8 = log5 t
21. The number of grams of a certain radioactive substance present at time t is given by
the formula y = 200C° wi t, where t is the number of years. How many grams are present
at time t = 0 ? How many grams are present at time t = 500 ?
doo
5
22. How long does it take for a deposit of $1000 to double at 8% compounded
continuously?
re,
,
23. A culture starts with 8600 bacteria. After one hour the count is 10,000.
a. Find a function that models the number of bacteria n (t) after t hours.
b. Find the number of bacteria after 2 hours.
c. After how many hours will the nwber of bacteria double?
(0
eilo co
e,
9 (4-)
)_
e_
15o)
to2.7 .q 1
1 e-
24. The half-life of radium-226 is 1600 years. Suppose we have a 22-mg sample.
itx.t,
a. Find a function that models the mass remaining after t years.
P.,
b. How much of the sample will remain after 4000 years?
c. After how long will only 18 mg of the sample remain?
e(k)
6) 's
25. The burial cloth of an Egyptian mummy is estimated to contain 59% of the carbon14 it contained originally. If the half-life of carbon-14 is 5730 years, how long ago was
the mummy buried?
5T3D
LI
26. The table below shows the coal production (in metric tons) from a small mine in
British Columbia.
a. Find a logarithmic model for these production figures.
b. Use the model to predict the coal production from this mine in 2008.
Year
Metric tons of coal
1950
1960
1970
1980
1990
2000
882
889
894
899
905
909
27. The table below gives the population of black flies in a closed laboratory container
over an 18-day period.
a. Find a logistic model for these data.
b. Use the model to estimate the time when there were 400 flies in the container.
Time(days)
0
Number of flies
10
2
4
6
8
10
12
16
18
25
66
144
262
374
446
492
498