MATH 107 QUIZ 5 I Professor: Dr. Jill Whealon NAME: _______________________________ I have completed this assignment myself, working independently and not consulting anyone except the instructor. INSTRUCTIONS · The quiz is worth 100 points. There are 8 problems. This quiz is open book and open notes. This means that you may refer to your textbook, notes, and online classroom materials, but you must work independently and may not consult anyone(and confirm this with your submission). You may take as much time as you wish, just turn in your quiz before the due date. · Show work/explanation where indicated. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is acceptable also. In your document, be sure to include your name and the assertion of independence of work. · General quiz tips and instructions for submitting work are posted in the Quizzes module. · If you need more room, just add it into the file. · If you have any questions about the quiz, please ask on the Discussion Board or email me at [email protected] 1. (8 pts) Which of these graphs represent a one-to-one function? Answer(s): ____________ (no explanation required.) (There may be more than one graph that qualifies.) (A) (B) (C) (D) 2. (8 pts) Based on data about the growth of a variety of ornamental cherry trees, the following logarithmic model about these trees was determined: h(t) = 5.18 ln(t) + 8.199, where t = age of tree in years and h (t) = height of tree, in feet. (Note that "ln" refers to the natural or base e log function) Using the model, at age 4 years, how tall is this type of ornamental cherry tree, to the nearest tenth of a foot? Show your work. 3. (4 pts) Which response converts 9x = 729 to a logarithmic equation? (no explanation required) 2. ______ A. log9 729 = x B. logx 729 = 9 C. logx 9 = 729 D. log9 x = 729 4. (16 pts) Solve the equation. Check all proposed solutions. Show work in solving and in checking, and state your final conclusion. 5. (12 pts) (a) log4 1 = _______ (fill in the blank) (b) Let State the exponential form of the equation. (c) Determine the numerical value of in simplest form. Work optional. 6. (12 pts) Let f (x) = x2 – x – 7 and g(x) = 3x + 2 (a) Find the composite function and simplify the results. Show work. (b) Find . Show work. 7. (20 pts) Let (a) Find f 1 , the inverse function of f. Show work. (b) What is the domain of f ? What is the domain of the inverse function f -1? (c) What is f (2) ? f (2) = ______ (d) What is f 1( ____ ), where the number in the blank is your answer from part (c)? Show your work 8. (20 pts) Let f (x) = ex – 1 + 2. Answers ...

1. MATH 107 QUIZ 5 I Professor: Dr. Jill Whealon
NAME: _______________________________
I have completed this assignment myself, working
independently and not consulting anyone except the instructor.
INSTRUCTIONS
· The quiz is worth 100 points. There are 8 problems. This quiz
is open book and open notes. This means that you may refer to
your textbook, notes, and online classroom materials, but you
must work independently and may not consult anyone(and
confirm this with your submission). You may take as much time
as you wish, just turn in your quiz before the due date.
· Show work/explanation where indicated. Answers without any
work may earn little, if any, credit. You may type or write your
work in your copy of the quiz, or if you prefer, create a
document containing your work. Scanned work is acceptable
also. In your document, be sure to include your name and the
assertion of independence of work.
· General quiz tips and instructions for submitting work are
posted in the Quizzes module.
· If you need more room, just add it into the file.
· If you have any questions about the quiz, please ask on the
Discussion Board or email me at [email protected]
1. (8 pts) Which of these graphs represent a one-to-one
function? Answer(s): ____________
(no explanation required.) (There may be more than one graph
that qualifies.)
(A)
(B)

2. (C)
(D)
2. (8 pts) Based on data about the growth of a variety of
ornamental cherry trees, the following logarithmic model about
these trees was determined:
h(t) = 5.18 ln(t) + 8.199, where t = age of tree in years and h
(t) = height of tree, in feet.
(Note that "ln" refers
to the natural or base e log function)
Using the model, at age 4 years, how tall is this type of
ornamental cherry tree, to the nearest tenth of a foot? Show
your work.
3. (4 pts) Which response converts 9x = 729 to a logarithmic
equation? (no explanation required) 2. ______
A. log9 729 = x
B. logx 729 = 9
C. logx 9 = 729
D. log9 x = 729
4. (16 pts) Solve the equation. Check all proposed solutions.
Show work in solving and in checking, and state your final
conclusion.

3. 5. (12 pts)
(a) log4 1 = _______ (fill in the blank)
(b) Let State the exponential form of the equation.
(c) Determine the numerical value of in simplest form.
Work optional.

4. 6. (12 pts) Let f (x) = x2 – x – 7 and g(x) = 3x + 2
(a) Find the composite function and simplify the results. Show
work.
(b) Find . Show work.
7. (20 pts) Let
(a) Find f 1 , the inverse function of f. Show work.
(b) What is the domain of f ? What is the domain of the inverse
function f -1?

5. (c) What is f (2) ? f (2) = ______
(d) What is f 1( ____ ), where the number in the blank is your
answer from part (c)? Show your work
8. (20 pts) Let f (x) = ex – 1 + 2.
Answers can be stated without additional work/explanation.
(a) Which describes how the graph of f can be obtained
from the graph of y = ex ? Choice: ________
A. Shift the graph of y = ex to the left by 1 unit
and up by 2 units.
B. Shift the graph of y = ex to the right by 1 unit
and up by 2 units.
C. Reflect the graph of y = ex across the x-axis
and shift up by 2 units.
D. Reflect the graph of y = ex across the y-axis
and shift up by 2 units.
(b) What is the domain of f ?
(c) What is the range of f ?

6. (d) What is the horizontal asymptote?
(e) What is the y-intercept? State the approximation to 2
decimal places (i.e., the nearest hundredth).
x
x
-
=
-
2
2
y
x
-
=
64
1
log
4
64
1
log
4
=
x
4
5
5
3
)
(

7. -
-
=
x
x
x
f
FOREIGN EXCHANGE MARKETS
Name:
…………………………………………………………………………
…….
Signature:
…………………………………………………………………………
…….
EXERCICE 1
1- Foreign Exchange Competitive exposure Risk:
1.1 Define Competitive Exposures
1.2 Define hedging techniques for competitive exposures.
1.3 Please describe the limits to the use of financial techniques
to hedge competitive risk
EXERCICE 2
Describe the USD currency performance (trade weighted broad)
https://fred.stlouisfed.org/series/DTWEXBGS9
against the rest of the world currencies during the last year in
terms of the Holy Trinity. Please note that the graph represents
the number of a basket of broad currencies that you need to buy
one dollar.
IMPORTANT: It is expected that you answer this question
using the following concepts: NER, RER, Inflation Rates in the
US and ROW, Net Exports (NX), Savings and Investments in
your comment applied to the USD relative to the rest of the
world.

8. EXERCISE 3
The US Company ZYZ has an account receivable in EUR: 10m
EUR, to be collected in 1 year.
Please use the following information to calculate the amount of
USD that it will receive if it hedges the EUR using forwards,
money market hedge and Options. On the option, will you
hedge using the call or the put option on the EUR? What
alternative provides a better outcome for XYZ?
At maturity of the forward and the option (one year) the
USD(EUR exchange rate (the sport) is trading at 1.15
USD/EUR. Will you exercise the option¿ Why? ,
Please describe
IMPORTANT INFORMATION : The quotes given are
(USD/EUR) (number of USD to buy one EUR, it is the book
convention).
The premium of the option is given in percentage of the amount
hedged. The Call option and the PUT option are on the EUR
(right to buy or sell the EUR)
Usaboys cost of capital is 5.0%.
Exhibit 1
---------------------------------------------------------------------------
----------
Spot
1.17

9. USD/EUR
Forward 1 year
1.185
USD/EUR
Interest Rate
-0,55%
EUR
Interest Rate
0,12%
USD
CALL 1 year Strike 1.185
6.8%
EUR
PUT 1 year Strike 1.19 7.9 % EUR
---------------------------------------------------------------------------
-----------
EXERCISE 4
Given the following USD/AUD quote (the number of AUD to
buy one USD),
Calculate the exchange rate appreciation or depreciation under

10. the two scenarios given below. USD/AUD spot today is 0.80. It
is important that you describe which currency appreciates or
depreciates and the percentage appreciation or depreciation of
that currency.
Scenario I: 0.75 USD/AUD
Scenario II: 0.94 USD/AUD
EXERCISE 5
John Scary Always, a market maker at Thanksobihelp! Bank in
the US, is managing a FX option book, including some exotic
options. John has received the call from one of his biggest
institutional clients, who wants to buy a structured note to get
$1m exposure to the EUR/USD, (the number of USD that you
need to buy one EUR
John trades in the structured note, selling the note (a digital or
Binary Option). The Barrier is at 1.21 EUR/USD.
The Delta exposure for seller of the exotic option are given in
the graph below (delta exposure)
(1) Please describe the Delta of the exotic option and the
required hedge the market maker will implement to be delta
Neutral (Zero; no directional exposure to the underlying
EUR/USD) using hedging instruments like futures that John will
have in his book. There is only one day to maturity and the
underlying currency pair is trading at 1.205 EUR/USD and
hasn’t touched the barrier during the life of the option if the
market maker decided to dynamically delta hedge the option
Delta using delta one instruments (futures)
(2) Now, once you have answered the previous question, please
imagine that the EUR appreciates further against the USD,
breaking the barrier above 1.21 EUR/USD.
Please describe the total Delta that John will have in its book
now that the option doesn’t exist any more, but the hedging
instruments are still in its book
Action? How does John get rid of directional risks once the
option does not exist anymore (knock out) and how does it
impact the currency market?

11. 13CitiFX Structuring
Market Commentary
M a n a g i n g D i g i t a l R i s k ( D e l t a )
Delta of a 1-month one touch 1.21, payout 1 mio EUR
Delta of a binary 1.21
0
20,000,000
40,000,000
60,000,000
80,000,000
100,000,000
120,000,000
140,000,000
160,000,000
1.12 1.14 1.16 1.18 1.20 1.22
1 month to expiry
2 weeks to expiry

12. 1 week to expiry
2 days to expiry
Close to the
trigger at expiry,
the Delta is
extremeNote
the
scale
Delta Hedge: Start by selling cash …until barrier is reached…