CorrectionKey=NL-A;CA-A CorrectionKey=NL-B;CA-B 16 DO NOT EDIT--Changes ...
16 M O D U L E
Study Guide Review
ASSESSMENT AND INTERVENTION
Assign or customize module reviews.
MODULE PERFORMANCE TASK
COMMON CORE
Mathematical Practices: MP.1, MP.2, MP.4, MP.6, MP.7 F-BF.5, F-LE.4
SUPPORTING STUDENT REASONING
Students should begin by thinking about how to find a model for the age of a carbon-containing material. They can then do research, or you can provide them with specific information. Here is some of the information they may ask for.
? What is the formula for radiocarbon dating?
Encourage students to derive this formula by
solving the half-life formula for t. The formula is
_t_
N
=
N
0(0.5)
,t_1_ 2
where
N
is
the
amount
of
C-14
currently in the sample, N0 is the original amount
of C-14, t_1_ is the half-life of C-14, and t is the 2
time in years.
? What is the half?life of carbon-14? 5,730 years
? Houghton Mifflin Harcourt Publishing Company
STUDY GUIDE REVIEW
Logarithmic Properties and Exponential Equations
Essential Question: How do the properties of logarithms allow you to solve real-world problems?
KEY EXAMPLE
(Lesson 16.1)
Simplify: log5 5x + 2 + log2 163.
Apply properties of logarithms.
log5 5x + 2 + log2 163 = (x + 2)log5 5 + 3log2 16 = (x + 2) + 3log2 (24)
= x + 2 + 3(4) = x + 14
KEY EXAMPLE
(Lesson 16.2)
Solve the equation: 43x + 1 = 6.
43x + 1 = 6
log43x + 1 = log6
Take the log of both sides.
(3x + 1)log4 = log6
Bring down the exponent.
3x
+
1
=
_ log6 log4
3x
=
_ log6 log4
-
1
Rearrange to isolate x.
( ) x
=
_ 1 3
_ log6 log4
-
1
0.0975
MODULE
16
Key Vocabulary
exponential equation (ecuaci?n exponencial)
Module 16
813
Study Guide Review
SCAFFOLDING SUPPORT A2_MNLESE385900_U6M16MC 813
? Remind students of the properties of logarithms:
_ loga (u v) = loga (u) + loga (v)
log a
u v
=
log a
(u)
-
log a
(v)
loga(un) = nloga(u)
loga(ab ) = b
? If students have trouble deriving the formula for carbon dating, you may wish
( ) to
provide
it:
t
=
t
_1_ 2
?
_llnn_(_0_NN.__50 _) .
The
meanings
of
the
variables
are
given
above.
3/29/14 2:22 AM
813 Module 16
EXERCISES Use properties of logarithms to simplify. (Lesson 16.1)
1. log_3 0.2164 5 12
3. log8 0.015625x -2x
2. log4 4x - 2 + log3 2432 x + 8
4. log102x + 1 + log3 9 2x + 3
Solve each equation. (Lesson 16.2)
5. 5x = 50
_lo__g_5_0_
log5
2.43
7. 202x + 3 = 15
( ) _1
2
_lo__g_1_5_
log20
-
3
-1.048
6. 6x + 2 = 45
_lo__g_4_5_
log6
-2
0.125
8. 35x + l = 150
( ) _1
5
_lo__g_1_5_0_ log3
-
1
0.712
MODULE PERFORMANCE TASK
How Old Is That Bone?
The La Brea Tar Pits in Los Angeles contain one of the best preserved collections of Pleistocene vertebrates, including over 660 species of organisms. An archeologist working at La Brea Tar Pits wants to assess the age of a mastodon bone fragment she discovered. She measures that the fragment has 22% as much carbon-14 as typical living tissue. Given that the half-life of carbon-14 is 5370 years, what is the bone fragment's age?
Start by listing in the space below the information you will need to solve the problem. Then use your own paper to complete the task. Be sure to write down all your data and assumptions. Then use graphs, numbers, words, or algebra to explain how you reached your conclusion.
SAMPLE SOLUTION
Assumptions
? The ratio of carbon-12 to carbon-14 in the atmosphere has been constant since the organism from which the sample originated died.
Method
Starting from the half-life formula, derive the formula for carbon dating by solving for t. Use the properties of logarithms.
N = N0 (0.5)t/t1/2
___N
N 0
=
( ) 0.5 t/t1/2
In
_N__
N 0
=
__t _
t_1
In
(0.5)
_ 2
t
=
t
_ 1
2
__In__N_N_0 _
In(0.5)
Use this formula, with t_1_ = 5730, N0 = 100, and 2
N = 22, to calculate the age of the fragment:
_ t = 5730 _I_n__12_02_0_ 12, 500 years In(0.5)
? Houghton Mifflin Harcourt Publishing Company
Module 16
814
Study Guide Review
DISCUSSION OPPORTUNITIES A2_MNLESE385900_U6M16MC.indd 814
? Do you think C-14 dating would be useful for finding the age of a dinosaur fossil? Why or why not?
? Why can't carbon dating be used to date stone tools?
29/03/14 8:01 PM
Assessment Rubric 2 points: Student correctly solves the problem and explains his/her reasoning. 1 point: Student shows good understanding of the problem but does not fully solve or explain. 0 points: Student does not demonstrate understanding of the problem.
Study Guide Review 814
Ready to Go On?
ASSESS MASTERY
Use the assessment on this page to determine if students have mastered the concepts and standards covered in this module.
ASSESSMENT AND INTERVENTION
Access Ready to Go On? assessment online, and receive instant scoring, feedback, and customized intervention or enrichment.
ADDITIONAL RESOURCES
Response to Intervention Resources ? Reteach Worksheets
Differentiated Instruction Resources ? Reading Strategies ? Success for English Learners ? Challenge Worksheets
Assessment Resources ? Leveled Module Quizzes
? Houghton Mifflin Harcourt Publishing Company
Ready to Go On?
16.1?16.2 Logarithmic Properties and Exponential Equations
Use properties of logarithms to simplify. (Lesson 16.1)
1. log_6 2.07365 5 20
2. log2 3.2 - log2 0.025 7
? Online Homework ? Hints and Help ? Extra Practice
3. log7 72x - 1 + log3 812 2x + 7
4. log5 125 - log105x -5x + 3
Solve each equation. Give the exact solution and an approximate solution to three decimal places. (Lesson 16.2)
5. 72x = 30
_ log30
2log7
0.874
6. 52x - 1 = 20
(_ ) log20
0.5
+ 1 1.431
log5
7. 20.5x + 7 = 215
(_ ) 2
log215 log2
-
7
1.496
8. 103x - 3 = 15
_ (_ ) 1
3
log15 log10
+
3
1.392
ESSENTIAL QUESTION
9. How do you solve an exponential equation algebraically?
Possible answer: Begin by taking the logarithm of both sides. This allows you to use the Power Property of Logarithms to bring down the variable, putting it in front of the logarithm. Then, use arithmetic operations to isolate the variable in the normal way. At the end of the process, you will likely need to use a calculator to find the value of a logarithmic expression.
815 Module 16
Module 16
815
Study Guide Review
COMMON CORE
Common Core Standards
A2_MNLESE385900_U6M16MC 815
Lesson Items Content Standards Mathematical Practices
16.1
1
F-BF.5
MP.7
16.1
2
F-BF.5
MP.7
16.1
3
F-BF.5
MP.7
16.1
4
F-BF.5
MP.7
16.2
5?8 F-LE.4
MP.2
3/29/14 2:22 AM
MODULE 16 MIXED REVIEW
Assessment Readiness
1. For each function below, determine if the function has an inverse defined for all real
numbers. Select Yes or No for A?C.
A. f(x) = 4x3 - 1
B. f(x) = 3x + 2
Yes
No
Yes
No
C. f(x) = 4x2 + 2
Yes
No
2. Consider the equation 8x+1 = 12. Choose True or False for each statement.
A. After bringing down the exponent,
the equation is (x + 1)log8 = log12.
True
False
B. The equation cannot be solved because the bases are not the same.
True
False
C. The approximate value of x is 0.195.
True
False
3. At a constant temperature, the pressure, P, of an enclosed gas is inversely proportional to the volume, V, of the gas. If P = 50 pounds per square inch when V = 30 cubic inches, how can you find the pressure when the volume is 125 cubic inches?
PV12ois5ssy=i.bTl_ e1h5aax0tn0ws,woseuorlx:dT=mhea1k2foe.rTtmhheeulafaimrysot=uenq_kxtucoaatfinporbnee3ssu0us=reed_ 5n.k0Ye,oesudoeckdan=isa11s52su0p0mo.euFnrPodimss xpt,hearenred, square inch.
4. A = P (1 + r)n gives amount A in an account after n years after an initial investment P that earns interest at an annual rate r. How long will it take for $250 to increase to $500 at 4% annual interest? Explain how you got your answer.
About 17.67 years; Possible explanation: Substitute, then use logarithms to solve for n:
500 = 250(1.04)n 2 = 1.04n
log 2 = nlog1.04
_ log 2 = n
log 1.04
17.67 n
16 M O D U L E
MIXED REVIEW
Assessment Readiness
ASSESSMENT AND INTERVENTION
Assign ready-made or customized practice tests to prepare students for high-stakes tests.
ADDITIONAL RESOURCES
Assessment Resources ? Leveled Module Quizzes: Modified, B
AVOID COMMON ERRORS
Item 1 Some students will miss that the item is asking about the inverse of each function. Remind students to read the entire question carefully, and highlight or underline key words.
? Houghton Mifflin Harcourt Publishing Company
Module 16
816
Study Guide Review
COMMON CORE
Common Core Standards
A2_MNLESE385900_U6M16MC 816
Lesson Items Content Standards Mathematical Practices
10.1, 15.1
1*
F-BF.5, F-BF.A
MP.1
16.2
2
F-LE.4
MP.2
8.1
3*
N-Q.2
MP.6
16.2
4
F-LE.4
MP.6
* Item integrates mixed review concepts from previous modules or a previous course.
8/20/14 9:21 PM
Study Guide Review 816
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
- essential question what are the properties of logarithms
- unit 5 worksheet 7 properties of logs
- unit 6 mod 16 1 properties of weebly
- exponential equation logarithmic equation chandler unified school
- section 4 4 logarithmic properties opentextbookstore
- intro to logarithms worksheet properties of simple logarithms
- properties of logarithms worksheet vealeymath
- worksheet logarithmic function department of mathematics
- correctionkey nl a ca a correctionkey nl b ca b 16 do not edit changes
- properties of logarithms fayetteville state university
Related searches
- a personality and b personality
- type a vs type b personality test
- bcps a day and b day schedule
- do or do not no try
- investing activities do not include the
- states that do not tax military pensions
- mba programs that do not require gmat
- do not like synonym
- type a and type b personality
- states that do not tax retirement income
- type a versus type b personality
- stocks that do not pay dividends