Question 4
1 / 1 point
Consider two bank accounts, one earning simple interest and one
earning compound interest. If both start with the same initial deposit
(and you make no other deposits or withdrawals) and earn the same
annual interest rate, after two
W04.11 4C Preparation Quiz
Question 1
1 / 1 point
In the savings plan formula, assuming all other variables are constant,
the accumulated balance in the savings account
A
increases as n increases.
)
B
increases as APR decreases.
)
C
decreases as Y increas
W04 4B Prep Quiz
Question 1
1 / 1 point
The annual percentage yield (APY) of an account is always
A
the same as the APR.
)
B
less than the APR.
)
C
at least as great as the APR.
)
Question 2
1 / 1 point
A bank account with compound interest exhibits what
Question 4
1 / 1 point
A rural population is falling at a rate of 20% per decade. If you wish to
calculate its exact half-life, you should set the fractional growth rate
per decade to
A
0.2.
)
B
20.
)
C
-0.2.
)
Question 5
1 / 1 point
Which of the followin
W04.11 4C Preparation Quiz
Question 4
1 / 1 point
The annual return on a 5-year investment is
Athe annual percentage yield that gives the same increase in the value
) of the investment.
B
the average of the amounts that you earned in each of the 5 years.
W03 8B Prep Quiz
Question 1
1 / 1 point
The population of an endangered species is falling at a rate of 7%
per year. Approximately how long will it take the population to drop by
half?
A
17 years.
)
B
10 years.
)
C
7 years.
)
Question 2
1 / 1 point
Radioa
Tossing a Biased Coin
Michael Mitzenmacher
When we talk about a coin toss, we think of it as unbiased: with probability one-half it comes up heads,
and with probability one-half it comes up tails. An ideal unbiased coin might not correctly model a real
co
1. Let x = ax + by and y = cx + dy.
H
y2
a) x =
= ax + by Hx = axy + b + (x).
y
2
x2
H
= cx + dy Hy = c dxy + (y).
y =
x
2
b 2
x2
1
Then, H(x, y) = axy + y c dxy = (a d)xy + (by 2 cx2 ).
2
2
2
1 2
1 2
1
2
If a = d, then H(x, y) = 2axy + (by cx ) = by 2ax
3.1.1: x = 1 + rx + x2
We set x = 0. Then, 1 + rx + x2 = 0.
So, x2 = rx 1.
Differentiating both sides with respect to x, we get:
r
2x = r. Thus, x =
.
2
Substituting x into 1 + rx + x2 = 0, we get:
r
r
1 + r( ) + ( )2 = 0. Thus, r = 2, 2 and x = 1, 1.
2
2
2.6.1: Explain the paradox: The book specifies that x = f (x) cannot oscillate in one dimensional
system in which they consider m
x negligible. In the homework problem, m
x = kx can be re-written
as m
x + 0x = kx in which this equation can oscillate. This
1
1
or q = .
2
2
A 2-cycle exists if and only if f (p) = q and f (q) = p. Equivalently, f (f (p) = p or f 2 (p) = p,
where f (x) = rx(1 x). Then (f (f (p)0 = f 0 (p)f 0 (f (p) = f 0 (p)f 0 (q) = 0. So, either f 0 (p) = 0 or
1
1
f 0 (q) = 0. We know that f
5.1.2: Proof:
x = ax
x(t) = c1 eat
y = y
y(t) = c2 et
dy
y
y
= =
dx
x
ax
dy
e(a+1)t
c2 eat
.
=
=
c
2
dx
ac1 eat
ac1
dy
c2
dy
Since a < 1, then a + 1 < 0. So,
when
> 0 and
dx
c1
dx
c2
when
< 0. Thus, the trajectories become parallel to the y-direction as
b) Given: N = rN
N
N
H
1
K
A+N
dN
F ish/T ime
dt
[H] F ish/T ime
[N ] F ish
[r] 1/time
[K] F ish
[A] F ish
Let =
t
d
1
. Then,
= .
T
dt
T
Let x =
N
dx
N
N
. Then,
= . So, x = .
k
dt
k
k
dx
N
=
dt
k
dx d
1 dx
dx
=
=
.
dt
d dt
Td
k dx
xk
xk
So,
= rxk 1
H
8.3.1) a) Find all the fixed points and use the Jacobian to classify them .
Let
x = 1 + (b + 1)x + ax2 y
and
y = bx + ax2 y
Then,
(b + 1)x 1
ax2
b
y = 0 y =
ax
x = 0 y =
So,
b
(b + 1)x 1
=
ax
ax2
bx = bx + x 1
x=1
Hence,
y=
b
a
b
Therefore, the fixed poin
2.4.4 : x = x2 (6 x)
The fixed points are: x = 0, 6
Using the analysis of stability, we get:
f 0 (x) = 2x(6 x) + x2 (1) = 2x(6 x) x2 = 3x(4 x)
At x = 6, we get f 0 (x) < 0. So, it is stable.
At x = 0. We get f 0 (x) = 0. So, we conclude nothing. Thus, we
1) Find a conserved quantity for the planar linear system:
x = 0 x(t) = c
y = 2x
m
x=
dV
dV
=
x = 0 V (x) = c
dx
dx
1
E = mx 2 + V (x) = 0 + c E = c = x
2
Thus, the conserved quantity is E = x.
Show that E has the properties of a conserved quantity.
E =
Financial ToolBoxes
(Gray-shaded boxes are the outputs based on the given inputs above them. Do not type in the shaded boxes.)
APR
Compounding Periods
Present Value
Payment
Years
Future Value:
APR
Compounding Periods
Present Value
Future Value
Years
Payme
Financial ToolBoxes
(Gray-shaded boxes are the outputs based on the given inputs above them. Do not type in the shaded boxes.)
APR
Compounding Periods
Present Value
Payment
Years
Future Value:
APR
Compounding Periods
Present Value
Future Value
Years
Payme
DESCRIPTIVE STATISTICS
Over the semester as you are taking Math 108, please keep track of your sleep hours (rounded to the nearest .5
Be sure to finish the descriptive statistics at the bottom and do a Copy / Paste of the table to your PowerPoint slid
Sem
Financial ToolBoxes
(Gray-shaded boxes are the outputs based on the given inputs above them. Do not type in the shaded boxes.)
APR
Compounding Periods
Present Value
Payment
Years
Future Value:
APR
Compounding Periods
Present Value
Future Value
Years
Payme
Sarah's Financial Action Plan
Sarah's Daily Expense Record
(* Do Not Type In Any Gray Boxes*)
Debit
Cash
February Budget
Income
Employment
Financial Aid
Other
Total Income:
Goal
290.00
125.00
100.00
415.00
Goal
Savings (Short Term)
Emergency
Living Expens
Math 313
Linear Algebra
Exam 2
Part I: Multiple Choice Questions: Unless otherwise stated, mark ALL answers which are correct for
each question.
1. (3.1) Find the determinant of A =
2
7
3 10
1
0 3 4
2 7
0
0
1 1
5
.
0
0
0
3
2
0
0
0
0
2
a)
36
b)
36
c)
4
Math 313
Linear Algebra
Practice Exam 1
Part I: Multiple Choice Questions: Mark all answers which are correct for each question.
1. Which of the following are solutions to the system below? Mark all that apply.
x1 + 3x2 + 4x3 = 7
3x1 + 9x2 + 7x3 = 6
a)
(1
Math 313
Linear Algebra
Practice Exam 3
Multiple Choice
1. Suppose = 2, 3 are eigenvalues and v, w are respectively the corresponding eigenvectors of an n n A. All the other eigenvalues of A
are either zero or not integers. Mark all the TRUE statements be
Work
Work
Whenever a force acts on an object over a distance, work is being
done.
Examples:
Example
Force
Distance
I pick up a backpack
The force of gravity = the weight From the floor to my shoulder
of the backpack.
I hit a golf ball.
The force exerted b
Volumes by Cylindrical Shells
Section 6.3
But First, Lets Review:
Set up, but do not evaluate, the
integrals that will yield the volume
of the solid of revolution when
the region to the right is:
Revolved around the x-axis
Revolved around the y-axis.
=