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 PreCalculus
Date 
Entry Task 
Activity and Journal Reflection 
Homework and Goals* 

3/10 
An employer tasks you to complete a job and
agrees to pay you $0.01 on day one, $0.02 on day two, and
$0.04 on day three, doubling the total amount on a given
day for an entire month. Complete the table using
the facts.

Exponential relationships:
Pressure vs. Altitude model relationship.

Today's Goal: Students will graph and interpret functions that are best characterized by exponential relationships. 

3/11 (Block) 
Select your preferred mathematics class for
next year HERE. What xvalue will give a yvalue of 3?

Differentiate between a power function and
exponential function. Graph (by hand!) Richter Magnitude vs. LOG(Energy). Use the graph to find the following (on the graph):
y = (first answer)*(second answer)^xWhat does this equation represent? Why? JR: What to power function and exponential functions have in common? How to power functions and exponential functions operate differently? 
Use the Laws of Exponents to explain the
following properties of the exponential function f(x)
= b^{x} using complete sentences.
Test Corrections: TODAY (AM/PM) Today's Goal: Understand the existence of a relationship between exponential functions and linear functions. (This relationship is the inverse) 

3/13 (Short) 
Independently complete the ET on a spare
sheet of paper, show all your work, turn this into Dr.
Edgerton: Assume, 2 = 10^{0.30103} Without using a calculator, find the value of x that will make the equation true.

Formal introduction of Logarithms:
JR: What are at least two things you would like to better understand about logarithms? Please be specific. 
Watch Khan
Academy Video about Logarithms Pg 113 # 1, 2, 3, 5 Today's Goal: Students will expand and formalize understanding of a logarithm of base 10. 

3/16 (6 Periods) 
What is an inverse function? What purpose
does it serve? Provide an example. 
Not
TreeLogs Activity  Understanding Logarithms JR: Explain what a logarithm is and why they are useful. 
Complete the lesson and HOMEWORK page
for today's activity. You will turn in today's homework
for credit. Today's Goal: Students gain familiarity with the logarithmic scale and the relationship between logarithms and exponential functions. Associated Standard: CCSS F.BF.5  (+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. 

3/17 (6 Periods) 
From last nights activity, Emily made a
claim about adding logarithms to multiply the numbers on
the power scale. Using the fact that 10^{log(x)} =
x, quantify the claims.

No
More Wood Logs Activity Change of Base Expand on the idea, show a proof of a different base and build understanding of the relationship between a base other than 10 and how to symbol manipulate. JR: Perform the following:

Problems 14 in homework packet (Extra Credit: On the log_{2} created in class, what does the point halfway between 0 and 1 represent. Explain.) Today's Goal: Students will be able to explain what "change of base" means and how they are calculated for logarithms other than base 10. Associated Standard: CCSS F.LE.4  For exponential models, express as a logarithm the solution to ab^{cx} = d where a, c, and d are real numbers 

3/18
(Block) 
Use your computer to do brief search of how
human kidney's operate. As best you can, explain the
process. 
It's
ALL in There Activity  Modeling Exponential
Functions Drug Filtering (NCTM) activity (modified to include several drug doses). EQ: How long does it take a drug to completely exit the body? (Hint: It doesn't leave the body... :O) JR: Describe a unique situation where you would use logarithms to solve for a real world problem. (Your situation should be different from all other students). 
All problems in homework packet
assigned 3/17 Today's Goal: Students will model an applicationbased scenario and use logarithms with nonstandard bases to solve for unknowns. Associated Standard: CCSS F.BF.5  (+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents 

3/20 (Short) 
Get ready for the quiz!

Quiz 2.1 (Exponents and Logarithmic Scale)
You may use a 3 x 5 note card* along with any measurement
devices you brought, but NO CALCULATORS Materials
will NOT be loaned during class. Topics on Quiz: Use logarithms to find the inverse of basic exponential functions; explain change of base in a new context; build exponential functions from a word situation. JR: What advice would you give to yourself at the beginning of this logarithms unit? 
Pg 130 #15, 16a and Pg. 132 # 2. Today's Goal: Assessing student's knowledge of logarithms and exponent relationships. 

3/23 
Change your calculator's graphing window to
the following settingsGraph:

Review concepts some students missed:
JR: Graph these pairs of functions separately on your calculator. What relationship do their graphs have?

Pg 137 # 3, 5, 11 Today's Goal: See the inverse relationship graphically between exponential functions and logarithmic functions. 

3/24 (Block) 
Explain the equivalence of these two statements: log_{b}a = x and b^{x}=a  Explore the nature of Euler's number. Convert between different forms of exponential functions (y = a·bx ⇒ y = a·emx ⇒ y = a·10nx). Use common ratios to model data with exponential functions. Pg. 128 #6, 7, 11. Pg. 148 Table 2.33 model with an exponential equation. convert to y = a·bx. Plot some of the data and the second exponential equation to check its fit. JR: Explain how you would create an exponential model if you are only given two data points. 
Given the two points (0, 4) and (3, 5.5):
http://betterexplained.com/articles/anintuitiveguidetoexponentialfunctionse/ 

3/25
(Assembly) 
Plot the following values in your
calculator and describe a function in the form y = a·e^{kx}
where a, k and x are constants.

Activity 2.7 (Pg. 144  148, Omit 1 and 2) JR: Explain the purpose of creating "semilog" and "loglog" graphs of data. What are the results of each? 
Pg 149 # 2, 4, 8, (Optional #12) Note: Reexpression is a way of rewriting an equation by manipulating a function with logarithms. Recall the semilog "reexpression" of the Richter scale on 3/11. Today's Goal: Students will learn techniques of exponential and logarithmic modeling. This includes using data to generate an exponential function and inverting to become logarithmic function. 

3/27 
Work at your fourtops and begin Activity
2.8 on page 155. 
Composition and Inverse Functions; Lesson
2.6. Activity 2.8 (Pgs. 155166) #12.
JR: Let f(x) = 2x + 1 and g(x) = 3x  7. Write the function f(g(x)) in simplest terms. 
Complete Today's activity AND One full page of notes on Pg. 157163 Today's Goal: Composition and Inverse Functions 

3/30 
Determine whether each of the following
sets of ordered pairs defines a function. If not, explain.
If yes, is it onetoone?

Composition Function Activity Pg 165 #4, 5, 7, 9, 10 JR: Explain the result should you expect by taking the composition of two functions that are inverses of one another? Provide some examples. 
Test Review Questions: Pg.171  177 # 3, 4 (sketch graphs), 6, 7, 8, 10, (optional 15). Today's Goal: Continue Composition functions, emphasis on domain and range 

3/31 
Model a function that passes through the
points (0, 32) and (100, 212) using a:

Inclass Review JR:Which skills do you need to review most for the test tomorrow? 
Finish review problems from yesterday's HW. Review session with Mr. G. immediately after class from 3:30pm  4:30pm. Today's Goal: Review for exam. 

4/1 (Block) 
Get ready for the Test!

Test 2.1 (No Foolin') You may use
YOUR calculator and a 3 x 5 note card* (writing on both
sides is permitted). Measurement devices (e.g. ruler
and protractor) are also allowed. No materials will
be loaned during class! Be prepared to:

Write the first 11 terms in the list as
fractions {1/0!, 1/1!, 1/2!, 1/3!, ..., 1/10!}. Then, add all of these numbers together in your calculator and express your result as a decimal (do not round.) If you continued making this sequence and adding numbers together, what value do you approach? 

4/3 
Use your calculator to model the data on p.
152 #12 (year vs. population) exponentially. Write
the equivalent logarithmic expression and use it to solve
for the year the population will reach 300,000,000.
Is your answer realistic? 
PostSpring Break Plans Review previous night's homework: Exponential functions as recursion:

Upon return, all Sophomores will miss class
14 class April 13, 14, 20 and 27 for the environmental
challenge fieldtrips. During this time, instruction will
continue and ALL prearranged absence procedures will be
followed according to the class
syllabus. Please review the class
syllabus if you are unclear on these procedures.
Week 1 of Quarter 4 is posted for your convenience. Otherwise, no additional homework assigned :) Today's Goal: Sequences and the relationship with exponential functions. 
Standard 
Description 
Notes 
F.LE.1.c 
Distinguish between situations that can be modeled with linear functions and with exponential functions.
Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.


F.LE.2 
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table).


F.LE.3 
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.


F.LE.4 
For exponential models, express as a logarithm the solution to abct =d where a ,c ,and d are numbers and the base b is 2,10,or e; evaluate the logarithm using technology.


F.LE.5 
Interpret the parameters in a linear or exponential function in terms of a context.


(P) F.BF.1.c 
(+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.


F.BF.4.b 
(+) Verify by composition that one function is the inverse of another.


F.BF.4.c 
(+) Read values of an inverse function from a graph or a table, given that the function has an inverse.


F.BF.4.d 
(+) Produce an invertible function from a noninvertible function by restricting the domain.


(P) F.BF.5 
(+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.


F.IF.7.e 
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★


N.RN.1 
Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.


N.RN.3 
Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

Students will model with exponential functions and
use data to find the function y = ab^{cx}
+ d and the inverse within an application context.
Students will calculate and use inverse and composition
functions for exponential, logarithmic, trigonometric and simple
polynomial functions.
Students will describe the domain and range of a function for
logarithmic, exponential, linear, polynomial, rational and
trigonometric functions.
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