ln〖e^0.05t=ln1600 〗
0.05t= ln1600
t= ln1600/0.05=147.56
b. ln(4x) =3

Answer: x= e^3/4

Show your work in this space:
e^ln4x =e^3
4x=e^3
x= e^3/4
c. log_2〖(8-6x)〗= 5
Answer: x=-4
Show your work in this space:
8-6x=2^5
-6x=32-8
-6x=24
x=-4
d. 4 + 5e^(‐x) = 0
Answer: No solution.
Show your work in this space:
5e^(-x)=-4
e^(-x)=-4/5
ln〖e^(-x) 〗=ln(-4/5)=undefined

Since the right side is undefined, there is no solution.

2) Describe the transformations on the following graph of f(x)=logx. State the placement of the vertical asymptote and x-intercept after the transformation. For example, vertical shift up 2 or reflected about the x-axis are descriptions.

a) g(x) = log( x + 5)
Description of transformation: The original function (f(x) = log x) is shifted to the left 5 units horizontally. Equation(s) for the Vertical Asymptote(s): x = -5
x+5=0
x=-5
X-intercept in (x, y) form: (-4,0)
Set g(x) = 0:
log(x+5)=0
x+5=〖10〗^0
x+5=1
x=-4
b) g(x)=log〖(-x)〗
Description of transformation: reflect about the y-axis
Equation(s) for the Vertical Asymptote(s): x = 0
-x=0
x=0
X-intercept in (x, y) form: (-1,0)
Set g(x) = 0:
log(-x)=0

-x=〖10〗^0

x=-1

3. Students in an English class took a final exam. They took equivalent forms of the exam at monthly intervals thereafter. The average score S(t), in percent, after t months was found to be given by S(t) = 68 - 20 log (t + 1),t ≥ 0.

What was the average score when they initially took the test, t = 0? Round your answer to a whole percent, if necessary

Answer: 68
Show your work in this space:
If t = 0 then
S(0)=68-20log〖(0+1)〗=68-20(0)=68-0=68
What was the average score after 4 month? After 24 months? Round your answers to two decimal places

Answer: S(4) = 54.02; S(24) = 40.04
Show your work in this space:
If t = 4...

...History of mathematics
A proof from Euclid's Elements, widely considered the most influential textbook of all time.[1]
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past.
Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. The most ancient mathematical texts available arePlimpton 322 (Babylonian mathematics c. 1900 BC),[2] the Rhind Mathematical Papyrus (Egyptian mathematics c. 2000-1800 BC)[3] and the Moscow Mathematical Papyrus (Egyptian mathematics c. 1890 BC). All of these texts concern the so-calledPythagorean theorem, which seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry.
The study of mathematics as a subject in its own right begins in the 6th century BC with the Pythagoreans, who coined the term "mathematics" from the ancient Greekμάθημα (mathema), meaning "subject of instruction".[4]Greek mathematics greatly refined the methods (especially through the introduction of deductive reasoning andmathematical rigor in proofs) and expanded the subject matter of mathematics.[5] Chinese...

...Week 5
Final Exam
Continuous schedule from Friday , November 1st. 9am until Saturday , November 2nd., 23:59pm.
Monday, November 4, 2013
20%
100%
To obtain the opportunity to take your final exam you should have delivered at least 6 activities.
Please keep this Agenda at hand so that you can deliver you assignments on time.
Greetings,
Blanca Alanís
Posted by: BLANCA HILDA ALANIS PENA
Posted to: CEL.HI09107V.343.13320 Inglés VII
Bibliography
Posted on: Thursday, October 3, 2013
Hello guys,
The books we are going to use are:
Text book:
Richards, Jack C. & Sandy, Chuck (2009). Passages 2 (2nd ed.). New York, N.Y. Cambridge University Press.
ISBN 978-0-521-68391-3
Workbook:
Richards, Jack C. & Sandy, Chuck (2009). Passages 2 (2nd ed.). New York, N.Y. Cambridge University Press.
ISBN 978-0-521-68393-7
Make sure they are the 2nd. edition, because the 1st. edition is completely different.
In your course, in the Bibliography Section you have a link of a bookstore where you can buy the books. You can try other bookstores in your city, of course, but they don't usually have the book in stock.
Greetings,
Blanca Alanís
Posted by: BLANCA HILDA ALANIS PENA
Posted to: CEL.HI09107V.343.13320 Inglés VII
Grading in the courseWeek 5
Final Exam
Continuous schedule from Friday , November 1st. 9am until Saturday , November 2nd., 23:59pm.
Monday, November 4, 2013
20%
100%
To...

...concrete model.
Looking on the locality of the paper, I highly acknowledge the fact that the researchers described the current state of math education in the Philippines. They emphasized the fact that we are more focused on procedural knowledge rather than the more desired conceptual knowledge. That is our disadvantage because we usually train students to perform math without understanding or making connections on what they are doing. By mentioning this, the readers would really have an idea that the paper itself could be a solution to the problem mentioned. Moreover, it makes the thesis more realistic.
To sum up everything that was tackled, I could say that the thesis served to have an important purpose in the current state of Mathematics Education in the Philippines. It is very informative and feasible. Since it is a small study because it only involved 6 average students, we could propose more studies rooting from this which would have a bigger scope such as implementing the same study but now comparing it to the results gathered from high and low performing students....

...HISTORY OF MATHEMATICS
The history of mathematics is nearly as old as humanity itself. Since antiquity, mathematics has been fundamental to advances in science, engineering, and philosophy. It has evolved from simple counting, measurement and calculation, and the systematic study of the shapes and motions of physical objects, through the application of abstraction, imagination and logic, to the broad, complex and often abstract discipline we know today.
From the notched bones of early man to the mathematical advances brought about by settled agriculture in Mesopotamia and Egypt and the revolutionary developments of ancient Greece and its Hellenistic empire, the story of mathematics is a long and impressive one.
Prehistoric Mathematics
The oldest known possibly mathematical object is the Lebombo bone, discovered in the Lebombo mountains of Swaziland and dated to approximately 35,000 BC. It consists of 29 distinct notches cut into a baboon's fibula. Also prehistoric artifacts discovered in Africa and France, dated between 35,000 and 20,000 years old, suggest early attempts to quantify time.
The Ishango bone, found near the headwaters of the Nile river (northeastern Congo), may be as much as 20,000 years old and consists of a series of tally marks carved in three columns running the length of the bone. Common interpretations are that the Ishango bone shows either the earliest known...

...SOLUTION GRADED ASSIGNMENT # 2 (5%)
This Assignment tests your knowledge of some aspects of course material covered in various
Topics. Prepare your response as a Microsoft Word document and submit in the Drop Box for
Assignment 2 before the closing time. All submissions must contained a signed Coursework
Accountability Statement declaring the work to be entirely yours. Assignments without the
Accountability Statement will not be marked.
The deadline for uploading this Graded Assignment is 3.30 pm (EC time) on Wednesday
November 5th, 2014.
Question 1 - Inequalities
A company makes two types of space-savers, english and italian. Each english type
requires 3 hours, 2 hours, and 2 hours, while each italian requires 2 hours, 1 hour, and
4 hours for cutting, assembling, finishing respectively.
The company has 300 hours available for cutting, 240 hours for assembling and
120 hours finishing . Each english type earns $85 in profit while the italian type earns $75.
a. If you are required to find the combinations of both types of space-savers that will
[6 mks]
maximize profits, list the inequalities that would be necessarry.
Let x be number of english type space-savers made and sold
Let y be number of italian type space-savers made and sold
3x + 2y ≤ 300
2x + y ≤ 240
2x + 4y ≤ 120
x ≥ 0, y ≥ 0
b. From a graph of the inequalities in part 𝑎. , − 𝐲𝐨𝐮 𝐚𝐫𝐞 𝐧𝐨𝐭 𝐫𝐞𝐪𝐮𝐢𝐫𝐞𝐝 𝐭𝐨 𝐬𝐮𝐛𝐦𝐢𝐭 𝐭𝐡𝐞 𝐠𝐫𝐚𝐩𝐡
[6 mks]
𝐢𝐧 𝐲𝐨𝐮𝐫 𝐚𝐧𝐬𝐰𝐞𝐫𝐬 − list the vertices of the...

...MATHEMATICS OF INVESTMENT
Simple Interest
If you borrow a car from a car rental company or if you live in someone else’s house or apartment, you have to pay rent. Like paying rent for the use of a car or a house, you also have to pay rent for the money you borrowed. This is called interest. People like Marco earn by charging interest on loans. Banks earn most of their income from the interest that people pay for the amounts they borrow. How much interest one has to pay depends on three factors: the principal, the time and the interest rate.
The principal is the initial amount borrowed. For example, if Marco lends Phillip P10,000, that amount would be the principal of his loan. The time, also known as term is the number of units expressed as days, months or years for which the principal was borrowed. In Marco’s case, he gives out loans with a term of 6 months. The interest rate or simply rate, is the percentage of the principal amount that the borrower has to pay for a term. For example, to get 5% of P100, multiply P100 by .05. 5% of P100 is P5.00. To get 30 % of P100, multiply P100 by .30. 30% of P100 is P30.00. This is the amount that a person has to pay as interest for the principal in a term. How is simple interest computed?
The formula for simple interest is:
I = PRT
Where I = interest
P = principal (the amount of money borrowed)
R = rate at which the interest is to be paid
T = term or length of time the debt (money owed) has to be paid...

...Semi-Detailed Lesson Plan in Mathematics (Transformations)
Level: First Year High School
Subjects: Mathematics, Geometry, Transformations
I. Objectives:
A. To recognize Euclidean transformations.
B. To recognize reflections, translations, and rotations.
C. To prove theorems related to transformations.
D. To solve problems involving transformations.
E. To apply transformations to real-world situations.
F. To create designs using transformations.
II. Materials:
papers, protractor, ruler
tangram puzzle
worksheets
III. Procedure:
A. Presentation
Activity - Folding of Paper
The teacher will give an activity that involves the folding of paper and tracing of shapes.
B. Discussion
From the activity, the teacher will point out that geometry is not only the
study of figures but is also the study of the movement of figures.
Is the original figure congruent to the other figures?
How does the second image compare to the original figure?
C. Input
Definitions:
Transformations
Reflection
Rotation
Translation
Dilation
Rigid Motion
Theorems:
Theorem 18-1
Theorem 18-2
Theorem 18-3
Theorem 18-4
C. Discussion
The above definitions and theorems will be discussed and proved. The teacher will ask the student to give examples of transformations.
D. Activity
Tangram Puzzle
The students will form six groups. Each group is going to make images of animals using tangram puzzle and they will identify the...