section 1 its other 2 parts to this whole assignment!!!!!

Step 1: **Watch the following video**.

Step 2: Then answer **one set of questions** listed below. Answers should be written as an essay using complete sentences, proper grammar, and correct spelling.

Click on “Reply” below. Then, type your essay into the box provided. When you are finished, click on “Post Reply” at the bottom right.

Step 3: After you have posted your response, then read your classmates’ posts and **respond to 2 other students’ posts** – 1 response should be to a student who chose to answer the same question set that you chose and 1 response should be to a student who chose to answer a different question set than you chose.

Click on “Reply” at the bottom left in the box of the classmate to whom you are responding. Then, type your response into the box provided. When you are finished, click on “Post Reply” at the bottom right.

TEST CORRECTION FORM

Name _____________________________________________Date: ___________________ Period: _______

Title of Assessment: _______________________________________________________________________

Original Assessment Score: __________ + __________ Points Back = __________ New Assessment Score

Directions: You MUST follow all steps completely and accurately for me to consider your test corrections for

re-grading. If the new answer is correct and accurately justified, you will earn back partial credit for previously

missed answer.

STEP 1: Identify the questions you missed. Write the question number in the Question Missed # (1) column.

Then write the letter of the answer you choose in the I choose Answer…(2)

STEP 2: Place the number that best fits the reason for missing the question in the WHY? (3) column, for the

questions you missed.

1) I didn’t understand the question

2) I thought I had this right

3) I studied this but forgot

4) I had no clue about this

5) I ran out of time or guessed

6) I made a careless mistake

STEP 3: Correct the question you missed by writing your new answer in the Correct Answer (4) column. Then

justify why this is now the correct answer in the Why is the new answer correct? (5) column. It is not sufficient

to write I found it in my notes or I remember you told me. Explain where you got the answer and why the new

answer is correct.

*If any part is missing or incorrect, NO credit is given for that correction.

1

Question

Missed #

2

I choose

Answer…

The letter of the

answer you chose

first.

3

4

Why?

Correct

Answer

Choose a number

from the options

above.

The letter of your your

new answer.

5

Why is the new answer correct?

Example: I said the object could speed up or slow down. However, the question says that the

object is moving at a constant speed. This means the speed is not changing so only the

direction can change

*DON’T use I didn’t study, or I didn’t know

©Shep’s Social Studies Resources

1

Question

Missed #

2

I choose

Answer…

The letter of the

answer you chose

first.

3

4

Why?

Correct

Answer

Choose a number

from the options

above.

The letter of your your

new answer.

5

Why is the new answer correct?

Example: I said the object could speed up or slow down. However, the question says that the

object is moving at a constant speed. This means the speed is not changing so only the

direction can change

*DON’T use I didn’t study, or I didn’t know

©Shep’s Social Studies Resources

Math 1314

Lab Module 4

Name _____________________

Show all work for each of the following problems. Simplify and clearly indicate all answers.

1. Complete the table below (use fractions–not decimals!) and use it to graph the function f(x) = 3x.

x

y

9

8

y

7

6

5

4

3

2

1

–2

–1

-9 -8 -7 -6 -5 -4 -3 -2 -1

-1

-2

Domain _______________

1 2 3 4 5 6 7 8 9

x

-3

-4

-5

-6

-7

-8

-9

0

Range ________________

coordinates of the y-intercept ____________

1

equation of the asymptote _____________

2

2. Using your knowledge of inverses, prepare a table of values for the inverse of the function in

problem #1.

Graph the inverse on the same coordinate system as the function.

Label each graph appropriately as f(x) or f-1(x).

Answer the following for the inverse function:

The equation of the inverse is f-1(x) = ______________

x

y

Domain _______________

Range ________________

coordinates of the x-intercept ____________

equation of the asymptote ____________

Math 1314

3.

Lab Module 4

page 2

Linda invests $3000 in a bond trust that pays 8% interest compounded monthly. Her friend

Lyla invests $3000 in a certificate of deposit that pays 7.75% compounded continuously.

For Linda:

a. State which formula should be used to solve this problem.

_____________________

b. Write the function for Linda.

_____________________

c. Determine how much Linda would have in her account after 20 years.

Work:

Linda’s amount:

_____________________

For Lyla:

a. State which formula should be used to solve this problem.

_____________________

b. Write the function for Lyla.

_____________________

c. Determine how much Lyla would have in her account after 20 years.

Work:

Lyla’s amount:

Now, determine who has more money after 20 years, Linda or Lyla?

_____________________

_____________________

Math 1314

Lab Module 4

page 3

4. The population of Collin County, which follows the exponential growth model, increased from

491,675 in 2000 to 782,341 in 2010.

a. Find the exponential growth rate, k. Don’t round, instead use the exact value of the growth

rate.

b. Write the exponential growth function. Use the exact growth rate found in a.

c. What should the population be in 2016? Use the function from b. Write your answer in a

complete sentence with proper grammar and correct spelling.

d. When should the population be 999,999? Use the function from b. Write your answer in a

complete sentence with proper grammar and correct spelling.

e. How long will it take the population to double? Use the exact growth rate found in a. Write your

answer in a complete sentence with proper grammar and correct spelling.

Math 1314

Lab Module 4

page 4

For the following problems, use the exact rates. Write your final answers in a complete

sentence with proper grammar and correct spelling.

-0.3h

5. The function D(h) = 8e

can be used to find the number of milligrams D of a certain drug

that is in a patient’s bloodstream h hours after the drug has been administered.

a. How many milligrams will be present after 4 hours?

b. When the number of milligrams reaches 1, the drug is to be administered again. After how

many hours will the drug need to be administered?

6.

A radioactive isotope, selenium, used in the creation of medical images of the pancreas,

has a half-life of 119.77 days. If 100 milligrams are given to a patient, how many milligrams

are left after 20 days?

7.

The Lualailua Hills Quadrangle of the East Maui (Haleakala) volcano on the island of

Maui in Hawaii is no longer active. To find out the date of the last eruption, scientists

conducted a chemical analysis of samples from the volcano area. The samples

contained approximately 62.31% of its original carbon-14. How long ago was the last

eruption of the volcano? (Use 5730 years for the half-life of carbon-14.)

Math 1314

Lab Module 4

page 5

8. Cryptology is the science of making and breaking codes. This lab explores how the idea of

functions and their inverses can be used to encode and decode messages.

To encode and decode a message, first replace each letter of the alphabet with a positive integer

using the following scheme, thus rewriting the original message as numbers instead of words:

A–1

F–6

K – 11

P – 16

U – 21

Z – 26

B–2

G–7

L – 12

Q – 17

V – 22

Blank – 27

C–3

H–8

M – 13

R – 18

W – 23

D–4

I–9

N – 14

S – 19

X – 24

E–5

J – 10

O – 15

T – 20

Y – 25

ENCODING: A one-to-one function can be used to encode a numerical message.

For example, suppose you want to send the message MATH to a friend, and you have decided

that the function f(x) = 3x + 4 will be the encoding function. This function simply describes the

procedure used to create the encoded message – in this case multiply by 3 and add 4. First

change the letters to corresponding numbers as shown above: 13 1 20 8. Then use these as the

input values in f(x).

f(13) = 3(13) + 4 = 43

f(1) = 7

f(20) = 64

f(8) = 28

So the encoded message that you send to your friend is: 43 7 64 28

NOTE: A graphing calculator can be used to evaluate a function as above:

a. Press [Y=] on the calculator. Type 3x + 4.

b. Choose [2nd][WINDOW] (TBLSET). Set the independent variable to Indpnt: Ask.

c. Then choose [2nd][GRAPH] (TABLE). Input each x value (13 1 20 8). The calculator

will return the function values (43 7 64 28) which is the encoded message.

DECODING an encoded message: Now it is up to your friend to decode the message. Decoding

is the process that “undoes” the encoding process. If f(x) encodes the message, what will decode

it? The inverse of f(x) or f-1(x)! So f-1(x) will be the decoding function.

x−4

In the example, the inverse of f(x) = 3x + 4 can be shown to be f-1(x) =

. Take the encoded

3

message (43 7 64 28) and use these values as input values in f -1(x). Again, the calculator can

x−4

be used to decode – simply enter y =

and use the TABLE feature as described above.

3

f-1(43) = 13

f-1(7) = 1

f-1(64) = 20

f-1(28) = 8

That’s the original numerical message! The last step is to convert back to letters using the table

given previously. Now your friend knows the message that you sent: MATH.

Math 1314

Lab Module 4

page 6

Cryptology Applications:

8.1. Suppose f(x) = 6x – 2 is the encoding function.

a. Encode “Collin Cougars”. [The answer will be numbers. Remember to include the space.]

Code: _____________________________________________________________________

b. Find the inverse of f(x).

c. Using the inverse function you just found, decode the following encoded message. Write the

letters above the numbers in the code. [The answer should be words. Put spaces where

appropriate!]

16 88 70 70 28 40 28 160 4 70 40 28 10 106 4 160 52 112 160 76

148 160 34 4 130 88 106 52 118 28 160 112 124 10 58 28 16 118

d. Why is it necessary for the encoding function to be one-to-one? Explanations should be

specific to this assignment, as well as clearly and thoroughly written using complete

sentences, correct spelling and proper grammar.

Math 1314

Lab Module 4

page 7

8.2. You intercepted the following message from Boris and Natasha.

25 19 19 30 41 17 15 26 27 41 15 28 18 41 18 29 41 34 22 19 41 27 15 34 22

You do not know the encoding or decoding function but from previous work with Boris and Natasha

you know their encoding and decoding functions are always linear and have 1 as the coefficient of x.

You also know this message consists of 6 words.

Using the encoding system described above,

a. How would you decode the message? Explain your strategy in complete sentences using

proper grammar and correct spelling.

b. Identify the decoding function.

c. What is the message?