Pre-Calculus
Calendar for February 21 to March 22, 2010
Date
Monday
2/21
Tuesday
2/22
Wednesday
2/23
Objectives
TSW evaluate logarithm and solve basic
logarithmic equations.
TSW use Logarithm Laws to expand or
condense a logarithmic expression.
TSW use Logarithm Laws to solve
equations.
Lesson
Evaluating Logarithms
Assignment
Worksheet
Condense and Expand Logarithms
Worksheet
Solve Logarithm Equations
Worksheet
Thursday
2/24
TSW use Logarithm Laws to solve
equations.
Worksheet
Friday
2/25
TSW will graph Logarithm equations
with transformations.
Solve Logarithm Equations
Quiz on Evaluating and
Condense/Expand Logs
Graphing Logarithms
Monday
2/28
TSW solve logarithmic equations
Worksheet
Tuesday
3/1
Wednesday
3/2
Thursday
3/3
TSW have a work day periods 6, 7 when
ELA TAKS is completed.
TSW solve logarithmic equations
Solving Exponential Equations using
Logs
Quiz on Solving Logs
ELA TAKS
Solving Exponential Equations using logs
day 2
Applications of Logarithms (Interest)
Quiz on Solving Exponential equations
using Logs
Worksheet
Friday
3/4
TSW apply their understanding of
logarithms to solve real world growth and
decay word problems.
TSW apply their understanding of
logarithms to solve real world logistic,
cooling and pH word problems.
TSW come to class with review
questions.
TSW demonstrate mastery of objectives
in Pre-Calc. to date.
TSW demonstrate mastery of objectives
in this logarithm unit
TSW use calculators to determine the
sinusoidal regression equation given data.
TSW come to class with review
questions.
TSW demonstrate mastery of objectives
in Pre-Calc. for the 3rd nine weeks.
Applications of Logarithms
(Growth/Decay)
Worksheet
Applications of Logarithms (Logistics,
cooling, pH)
Worksheet
Review Test #4 Logarithms
Quiz Applications of Logarithms
DAC
Worksheet
Test #4: Logarithms
STUDY
Sinusoidal Regression
Have agreat
spring break.
Enjoy your
spring break
Print out Unit
5
Monday
3/5
Tuesday
3/8
Wednesday
3/9
Thursday
3/10
Friday
3/11
Monday
3/21
Tuesday
3/22
TSW apply their understanding of
logarithms to solve real world interest
word problems.
grade
Worksheet
Worksheet
Worksheet
STUDY
Review for 3rd Nine Weeks Test
3rd Nine Weeks Test
Monday, February 21
I. Evaluate.
1) log 2 32
2) log 9 27
3) ln e
4) log10 (0.001)
8) log 1 9
9) log 4 5 4
10) ln1
11) log36 6
6) log 7
5) log6 1
3
13) log 5
12) log5 25 5
3
15)
log 4 16
II Solve.
22)
16) ln
1
e3
log 4 x  3
17)
log 7 7
23) log 9 x 
18)
1
2
log16 2
24)
19)
log5 3 25
log x 8  3
20)
25)
7) ln
1
125
14) ln e e
ln e2 3 e
log 8 4  x
1
e
1
7
21)
log3
1
9
Tuesday, February 22
I. Condense - write as a single logarithm and, if possible, a rational number.
1
2
ln 8  2 ln 5
3)
4) log M  3log N
log5 2  log5 3  log5 4 2) log 2 48  log 2 27
3
3
1
1
5)
6) 5  log A  log B   2log C 7) log8 80  log8 5
8) ln 25  ln 2
 log M  log N  log P 
2
2
1)
II. Expand the given expression.
1
log 3 11x
11)
log 3 3 x  1
12)
log4 3x
5
x2
15)
log 5
16)
ln
log 4 (2 x  1)  log 4 ( x  2)  1
3)
log 4 ( x  4)  log 4 x  log 4 5
4) ln( x  1)  2
5) log x ( x  8)  log 2 x  log 2 6
6)
log3 x  log3 ( x  2)  1
7) ln( x  2)  3
8)
x
2
e
15) ln x  ln( x  3)  ln10
1
 5
x
16) log 6 ( x  2)  2
Thursday, February 24
Solve. State the domain.
1
1) 2log 6 4  log 6 16  log 6 x
4
4) log  x  3  log  x  1  log8
Solving Log Equations (Day 2)
9) ln
10)
t
z
17
13) log 2
14) ln
xy
x2 y
z7
Wednesday, February 23
Solving Log Equations (Day 1)
Solve. (answers can be left in terms of “e” if necessary) State the domain.
1)
log 2 ( x  2)  log 2 5  4
2)
2
11) ln
2ln x  8
9)
log x 64  3
3
13) ln x  ln( x  1)  ln 2
12) ln
2) log6 18  log6  x  2  2
8) log 6 x 
14)
(ln x)2  16
3) log x  log x  log x  log8
6) log5  x  2  log5  x  2  1
5) 3log7 4  4log7 3  log7 x
7) log2  4 x  10  log2  x  1  4
10) log 5  log x 2  2
10) ln x  18
1
1
log 6 9  log 6 27
2
3
11) log x  log 4  1
9) log 5  log x  1
12) log 3  log y  2
14) log 3  2 x  5   log 3  x 2  4 x  4   2
13) log  x 1  log  x  2  log12 12
15) log x  log  x  21  log5 25
16) log x 
1
 2 log 8  6 log 3  log 3  2 log 2
3
Friday, February 25 Graphing Logarithms
Graph each of the following log functions. Find the domain and the range, and the x and y intercepts.
Be sure to draw the vertical asymptotes.
h( x)  log3 ( x)  3
f ( x)   log 2 x
6) h( x)  log 3 ( x)
10) f ( x)  ln( x)
Monday, February 28
Solving Exponential Equations using Logs
1)
f ( x)  log 2 x
2)
g ( x)  2log 2 x
1) 2x  45
6) 10x6  250
2) 3x  3.6
7) 3e x  42
x
11) 300e 2  9000
12) 10000.12 x  25000
16) 8 12e x  7
17) 4  e2 x  10
Tuesday, March 1
3)
f ( x)  log 2 ( x  2)
f ( x)  log 2 ( x  1)  2
11) f ( x )  2 ln( x  4)
7)
y  log 2 x  2 5)
8) f ( x)   log3 x  3
12) f ( x)  2 ln x  3
4)
9)
Solve. (Round to three decimal places)
3) 102 y  52
4) 73 y  126
5) 3x 4  6
1
1
x
8) e x  5
9) e3 x  20
10) 250 1.04   1000
4
2
1
13)  4 x 2   300 14) 6  2x1  1
15) 7  e2 x  28
5
18) 32  e7 x  46
ELA TAKS 6th and 7th workday
19) 23  5ex 1  3
x


20) 4 1  e 3   84


Wednesday March 2
Solving Exponential Equations using Logs
Solve. (Round to three decimal places)
1) 3  24
2) 2  5  18
x
6) e
1
11)
7 8
2x
x
33  8
16) 7  2
x
7) 6
5x
x
3) 3  3  9
 3000
8) 3e
x 1
 80
13) e
2 x 3
2x
12) 3
5
17)
x
 27
 9
4) 2
x3
7
5)
9) 14  3e  11
x
14) 4
3 x
 0.10
5(10 x6 )  7
10)
3(5x1 )  21
15)
12x  1  11
3000
2
2  e2 x
Factor the following and solve. (Round answers to three decimal places)
18) e
2x
 4e x  4  0
Thursday, March 3
19) e
2x
 5e x  6  0
20) e
2x
 3e x  4  0
Interest Word Problems
1) Find the amount of money that results if $100 is invested at 4% compounded quarterly for 2 years.
2) A sum of $1500 was invested for 5 years, and the interest was compounded monthly. If this sum amounted to $1633 in the given
time, what was the interest rate? compounded quarterly after a period of 2 years.
3) Find the amount of money that results if $100 is invested at 10% compounded continuously for 2.25 years.
4) Find the principal needed to get $600 after 2 years at 4% compounded quarterly.
5) Find the principal needed to get $1000 after 1 year at 12% compounded continuously.
6) Find the principal needed to get $800 after 3.5 years at 7% compounded monthly.
7) If Tanisha has $100 to invest at 8% per annum compounded monthly, how long will it be before she has $150? If the compounding is
continuous, how long will it be?
8) How many years will it take for an initial investment of $25,000 to grow to $80,000? Assume a rate of interest of 7% compounded
continuously.
9) Jerome is buying a new car for $15,000 in 3 years. How much money should he ask his parents for now so that, if he invests it at
5% compounded continuously, he will have enough to buy the car?
10) A business purchased for $650,000 in 1995 is sold in 1998 for $850,000. What is the annual rate of return for this investment?
Friday, March 4
Growth and Decay Word Problems
1) The size of P of a certain insect population at time t (in days) obeys the equation P  500e
population reach 1000? When will it reach 2000?
2) Strontium-90 is a radioactive material that decays according to the equation: A  Ao e
and A is the amount present at time t in years.
grams of strontium-90 to decay to 10 grams.
0.02 t
0.0244t
a) What is the half-life of strontium-90?
. After how many days will the
, where
Ao is the initial amount present
b) Determine how long it takes for 100
3) The population of a colony of mosquitoes obeys the law of unihibited growth. If there are 1000 mosquitoes initially and there are
1800 after 1 day, what is the size of the colony after 3 days? How long will it take until there are 10,000 mosquitoes?
4) A culture of bacteria obeys the law of uninhibited growth. If 500 bacteria are present initially and there are 800 after 1 hour, how
many will be present in the culture after 5 hours? How long is it until there are 20,000 bacteria?
5) The population of a southern city follows an exponential model If the population doubled in size over an 18 month period and the
current population is 10,000, what will the population be 2 years from now?
6) The half-life of radium is 1690 years. If 10 grams are present now, how much will be present in 50 years?
7) A piece of charcoal is found to contain 30% of the carbon-14 that it originally had. When did the tree from which the charcoal came
die? Use 5600 years as the half-life of carbon-14.
8) The half-life of radium is 1690 years. If 28 grams are present now, how much will there be in 25 years?
9) If 1000 grams of a radioactive element decays to 825 grams in 50 days, what is its half-life?
10) When some radioactive element was released into the air, it was absorbed into the bones of people in the area. If the half-life of this
element is 12 years, what fraction of the element remained in their bones 5 years later? Assume that the original amount is 1.
Monday, March 7
Logistics, cooling and PH problems
1) A pizza baked at 450°F is removed from the oven at 5pm into a room that is a constant 70°F. After 5 minutes, the pizza is at 300°F.
a) Find k. b) At what time can you begin eating pizza if you want its temperature to be 135°?
2) A thermometer reading 72°F is placed in a refrigerator where the temperature is a constant 38°F. If the rate of cooling is -.218°, what
will it read after 7 minutes? Find the time it will take before the thermometer reads 39°F.
3) A thermometer reading 8°C is brought into a room with a constant temperature of 35°C. If the thermometer reads 15°C after 3
minutes, what will it read after being room for 5 minutes?
4) A frozen steak has a temperature of 28°F. It is placed in a room with a constant temperature of 70°F. After 10 minutes, the
temperature of the steak has risen to 35°F.
a) Find the k value.
b) What will the temperature of the steak be after 30
minutes?
c) How long will it take for the steak to thaw to a temperature of 45°F?
5) The logistic growth model
P (t ) 
0.90
1  3.5e 0.339t
relates the proportion of new personal computers sold at Best Buy that have
Intel’s latest coprocessor t months after it has been introduced. a) What proportion of new personal computers sold at Best Buy will
have Intel’s latest coprocessor when it is first introduced (that is, at t=0). b) Find the maximum proportion of new personal computers
sold at Best Buy that will have Intel’s latest coprocessor. c) When will 75% of new personal computers sold at Best Buy have Intel’s
latest coprocessor?
6) The logistic growth model P (t ) 
1000
1  32.33e  o.439t
represents the population of a bacteria after t hours.
capacity of the environment? b) What was the initial amount of bacteria in the population?
bacteria be 800?
a) What is carrying
c) When will the amount of
7) Often environmentalists will capture an endangered species and transport the species to a controlled environment where the species
can produce offspring and regenerate its population. Suppose that six American Bald Eagles are captured and transported to Montana
and set free. Based on experience, the environmentalists expect the population to grow according to the model
P (t ) 
500
1  83.33e 0.162t
a) What is the carrying capacity of the environment? b) What is the predicted population of the American Bald Eagle in 20 years? c)
When will the population be 300?

8
8) The hydrogen ion concentration of a sample of human blood was measured to be  H   3.16  10 . Find the pH and classify the
blood as acidic or basic.
9) The hydrogen ion concentration of a sample of lemon juice is given. Calculate the pH.
 H    5.0 103
10) Salt (NaCl) decomposes in water into sodium and chloride ions according to the law of uninhibited decay. If the initial amount of
salt is 25 kilograms and after 10 hours, 15 kg. of salt is left, how much salt is left after 1 day?
11) The voltage of a certain conductor decreases over time according to the law of uninhibited decay. If the initial
volts and the rate of decrease is -.693, what is the voltage after 5 seconds?
voltage is 40
12) After the release of radioactive material into the atmosphere from a nuclear power plant at Chernobyl in 1986, the hay in Austria
was contaminated by iodine-131. Its half-life is 8 days. If it is all right to feed the hay to cows when 10% of the iodine-131 remains,
how long do the farmers need to wait to use this hay?