Asgn I
1
1. Craps. In the game of craps, a player rolls two balanced dice. Thirty-six equally likely
outcomes are possible, as shown in Fig 4.1 (in our textbook). Let
A = event the sum of the dice is 7
B = event the sum of the dice is 11,
C = event the su
Lecture 6.1: Supplementary Example
A sum of $1000 is invested at an annual rate of 8%. Find the compound amount after 2 years
when interest is compounded:
a. annually
1000(1 0.08) 2 1166.4 dollars
d. monthly
b. semiannually
e. weekly
1000(1
0.08 22
) 116
EELC291
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Confidence
Lecture 3
Sensation and Perception
Tieyuan Guo
Lecture 3 Outlines
Sensory Knowledge of the World
The Visual System
Hearing
Your Other Senses
Organizational Processes in
Perception
Identification and Recognition
Processes
What is Perception?
Perception
Def
Lecture 1 - Examples
Lecture 1: Supplementary example
Given the following relationship between
x and y :
x
13
5
0
2
10
y
7
0
10
0
120
a. Is y a function of x ? Why?
b. Is x a function of y ? Why?
Ans:
a. Yes, y is a function of x . For each input x , t
Lecture 2 - Examples
Lecture 2: Example 1
Suppose that the consumer demand for a commodity is a linear function of its price. If the price
is $24 per unit, 60,000 units can be sold. If the unit price is $32 per unit, 44,400 units can be
sold.
a. Determine
Solutions to Class Exercise 3
1.
Let V f (t ) V0 e kt be the amount of radioactive element:
V f (30) 48e k 30 6
e k 30
1
8
ln e k 30 ln
30k ln
1
8
1
8
k 0.069315
V f (t ) 48e 0.069315t
To get the elements half-life:
1
V f (t ) 48e 0.069315t 48
2
1
e 0.
Lecture 8
Instantaneous Rate of Change
The average rate of change of f with respect to x, as x changes from
x1 to x 2 , is the ratio
f ( x1 x ) f ( x1 )
.
x
The instantaneous rate of change of f with respect to (w.r.t) x, at x1
, is the limit of the above
Lecture 12 Optimization and Practical Optimization
Absolute extrema
The absolute maximum of a function on an interval is the largest value of
the function on the interval.
The absolute minimum is the smallest value of the function on the interval.
Extreme
QMDS100 Business Mathematics
Second Semester 2015/2016
Suggested Answers to Midterm Examination
Answers of Section A (Yellow Paper)
Qn. No.
Answer
Qn. No.
Answer
1
B
6
A
2
C
7
D
3
C
8
D
4
D
9
A
5
B
10
A
3
B
8
B
4
A
9
B
5
C
10
C
Answers of Section A (Pink
BECO 101 Principles of Macroeconomics
Assignment 2
1. Describe the effect on total output for a $30 billion increase in the money supply under
these conditions:
A) a $60 billion increase in the money supply reduces the interest rate by 1%,
B) a 1% decreas
Student
Submission
Number:
FACULTY OF BUSINESS ADMINISTRATION
QMDS 100 BUSINESS MATHEMATICS
ASSIGNMENT THREE
Due date & time: : April 20, 2016 (2:15pm-4:30pm)
Submitted to: Mr. Edmund Guo (E22-1046)
Student Number:
Student Name:
Section Number:
Instructor
FACULTY OF BUSINESS ADMINISTRATION
QMDS 100 BUSINESS MATHEMATICS
ASSIGNMENT THREE SOLUTIONS
Section A
1. Correct choice: a
7
f ( x ) x3 2 x 2 3x 1
3
andfiscontinuousover[0,3]
f ( x ) 7 x 2 4 x 3 (7 x 3)( x 1)
Theonlycriticalvalueon[0,3]is
3
x
7
.Wehavef(0
QMDS 100 - BUSINESS MATHEMATICS
SOLUTIONS TO PROBLEM SET
Lecture 1 - Linear and quadratic functions
1. (a). No, the price is not a function of the quantity sold because one domain
corresponds more than one range in a function.
(b). No. (The reason is the
Lecture 5 - Examples
Lecture 5: Example 2
Suppose the population of a developing country grows exponentially at the rate of 5% p.a. How
long will it take to double the countrys present population?
Ans:
Let V f t be the population in t years time
V f t V0
Lecture 3 - Examples
Lecture 3: Supplementary example 1:
It costs $2200 to produce 30 units of a commodity while it costs $4200 to produce 70 units. Find the
linear cost function, expressing the total cost in terms of the number of units produced.
Ans:
Le
Lecture 6.3 - Examples
Lecture 6.3: Supplementary Example 1
A person is going to make the following savings:
$1000 at the end of the first month,
$2000 at the end of the third month and
$3000 at the end of the six month
Assuming an interest rate of 12% co
Lecture 6.2 - Examples
Lecture 6.2: Example 1
Determine the present value of a $500 due in 10 years at a 6 percent discount rate
compounded annually.
Ans:
S P 1 i
P
t
S
500
279.1974 279.2 dollars
t
(1 i )
1 0.0610
Lecture 6.2: Example 2
Ms. Choy wishes t
Student
Submission
Number:
FACULTY OF BUSINESS ADMINISTRATION
QMDS 100 BUSINESS MATHEMATICS
ASSIGNMENT TWO
Due date & time: March 17, 2017 (2:15pm-4:30pm)
Submitted to: Ms. Xu Dan (E22-1048-13)
Student Number:
Student Name:
Section Number:
Instructor Name
Lecture 14 - Examples
Lecture 14: Example 1
x
5
9
6 5 x 4 dx
Ans:
x
5
du
dx
dx
du 5 x 4 dx
du
Let u x 5 6
u 10
c
10
( x 5 6)10
c
10
9
6 5 x 4 dx u 9 du
Lecture 14: Example 2
x
2
3
e x dx
Ans:
Method 1: Let u x 3
x
x
2
2
du
dx
dx
du 3 x 2 dx
1
du x
Lecture 13 - Examples
Lecture 13: Example 10
A companys marginal cost function is 0.015 x 2 2 x 80 (dollars per unit), where x denotes
the number of units produced in one day. The company has fixed costs of $1000 per day.
a. Find the cost of producing x u
Lecture 10 - Examples
Lecture 10: Example 1
dy
if y 5u 3 and u x 2 x 3 .
dx
Compute
Ans:
dy dy du
15u 2 ( 2 x 3 x 2 ) 15 x 2 x 3
dx du dx
2 x 3x
2
2
Lecture 10: Example 2
The total cost, C (in thousand of dollars), of producing x (in hundred) units of
Lecture 7 - Examples
Lecture 7: Supplementary Example 1
Find the derivative of f x
x
.
ln x
Ans:
1
ln x 1 x
x ln x 1
f x
2
(ln x)
ln x 2
Lecture 7: Supplementary Example 2
Determine the derivative of the following function:
10 x
f x
ln x
Ans:
1
ln x
Student
Submission
Number:
FACULTY OF BUSINESS ADMINISTRATION
QMDS 100 BUSINESS MATHEMATICS
ASSIGNMENT THREE
Due date & time: : November 18, 2016 (2:15pm-4:30pm)
Submitted to: Mr. Edmund Guo (E22-1046)
Student Number:
Student Name:
Section Number:
Instruc
Lecture 10: Example 1
dy
if y 5u 3 and u x 2 x 3 .
dx
Compute
Ans:
dy dy du
15u 2 ( 2 x 3 x 2 ) 15 x 2 x 3
dx du dx
2 x 3x
2
2
Lecture 10: Example 2
The total cost, C (in thousand of dollars), of producing x (in hundred) units of some commodity is
give
BECO100 001-003 Principles of Microeconomics
ASSIGNMENT 1
1. Suppose that a consumer spends recreation time and income on two leisure activities:
tennis and fishing. The consumer has the basic equipment to pursue both activities.
The costs associated with