MTHH040059 University of Nebraska Logarithmic Forms and Equations Paper

Hello,

I need this test finished entirely. The only questions that do not need to be answered are; 35, 36, 39, 42, 43, 44, 45, 47, 48, and 50.

No textbook is required, however, it would be best to have a graphing calculator handy.

This should be a fairly easy test, especially if you have knowledge of this subject.

Thank you,

B

Course Name: Second Year Algebra 2
Student: Alexandra Stratemann
Course ID: MTHH040059
ID: D81334747
Submittal: 51
Progress Test 1
Although the progress test is similar in style to the unit evaluations, the progress test is a closed-book test. It is
important that you do your own work. Select the response that best completes the statement or answers the question.
Your graphing calculator may be used on this progress test. You may also use scratch paper to work out the solutions.
____ 1.
____ 2.
Expand the logarithm logb 5x 4y 3.
a.
logb 5 + logb 4x + logb 3y
b.
logb 5 + 4 logb x + 3 logb y
c.
logb 5 + logb x 4 + logb y 3
d.
5 logb x 4 + 5 logb y 3
Which of the following describes the function y = 10x?
a.
b.
c.
d.
____ 3.
Solve the equation: log 8x = −3.
a.
b.
c.
d.
____ 4.
0.008
0.000125
−2.6
8000
Solve the equation
a.
b.
c.
d.
____ 5.
exponential decay
exponential growth
quadratic
linear
=
.
10
2
−2
−10
Which of the following describes the function y = 1.023(0.98)x?
a.
b.
c.
d.
exponential decay
exponential growth
quadratic
linear
____ 6.
____ 7.
Write a function that models inverse variation if x = −2 when y = −3.
a.
y=
b.
c.
y = −6x
d.
y = 6x
Classify this pair of events: A volleyball team is selected at random from the league; one of the remaining
teams is selected at random.
a.
b.
____ 8.
independent
dependent
Simplify the expression:
a.
b.
c.
d.
____ 9.
y=
.
x–3
x+5
x + 15
x–5
Solve the equation: ln 2 + ln 6 = x.
a.
b.
c.
d.
12
2.079
1.099
2.485
____ 10. How is the graph of y = log6 (x + 1) – 4 translated from the graph of y = log6 x?
a.
b.
c.
d.
right 1 unit and up 4 units
left 1 unit and up 4 units
right 1 unit and down 4 units
left 1 unit and down 4 units
____ 11. Expand the logarithm log (3mn)3.
b
a.
3logb (3mn)
b.
logb 9 + 3 log​b m + 3
logb n
c.
3(logb 3m + logb n)
d.
3(logb 3 + logb m + logb n)
____ 12. Solve the equation x +
a.
b.
c.
d.
24
−24
400
−400

= 25.
____ 13. Subtract and simplify:

.
a.
b.
c.
d.
____ 14. Solve the equation
a.
b.
c.
d.
____ 15.
=5+
.
5, −6
6, −5
−3, 2
−2, 3
What are the points of discontinuity of this function: y =
a.
b.
c.
d.
?
2, −2
4, −4
−4, 16
none
____ 16. Which exponential equation goes through the points (2, 128) and (−1, 16)?
a.
y = 64(2)x
b.
y = 32(2)x
c.
y = 16(2)x
d.
y = 8(4)x
____ 17. What are the asymptotes of the function y =
a.
x=
,y=
b.
x=
,y=4
c.
d.
x = 3, y = 4
x=
,y=4
?
____ 18.
What are the points of discontinuity of this function: y =
a.
b.
c.
d.
?
4, −5
−4, 5
−4, −5
4, 5
____ 19. The population of Blinsk was 26,150 in 2000. In 2005, the population was 28,700. Find the growth function
P(x) that models the population.
____ 20.
a.
P(x) = 28,700(1.019)x
b.
P(x) = 26,150(5)x
c.
P(x) = 26,150(1.019)x
d.
P(x) = 28,700(5)x
Add and simplify:
+
.
a.
b.
c.
d.
____ 21. What are the points of discontinuity of this function: y =
a.
b.
c.
d.
−4
8
−4, −8
−8
____ 22. Write this expression in a single logarithm: log 4 + log 2 – log 5.
a.
b.
c.
log −30
log 1
d.
log −
____ 23. Write this expression in a single logarithm: log 2 + log 5.
a.
b.
c.
d.
log 2.5
log 10
log 7
log 25
?
____ 24. Write a function that models inverse variation if x = 2 when y = 7.
a.
y=
b.
c.
y = 14x
d.
y = −14x
y=
____ 25. The adult population of a city is 1,250,000. A consultant to a law firm uses the function P(t) = 1,250,000(1 –
e−0.03t) to estimate the number of people P(t) who have heard about a major crime t days after the crime
was first reported. About how many days does it take for 80% of the population to have been exposed to
news of the crime?
a.
b.
c.
d.
____ 26.
54 days
7 days
23 days
39 days
Simplify the expression:
÷
a.
b.
c.
d.
____ 27.
Write the equation
a.
−4 = 81
b.
log−4
c.
log81 −4 =
d.
= 81
81 = −4
= 81 in logarithmic form.
.
____ 28.
Simplify the expression:

.
a.
b.
c.
d.
____ 29. You place $800 in an investment account that earns 5% interest compounded continuously. Find the
balance after 4 years.
a.
b.
c.
d.
$977.12
$5911.24
$2183.92
$646.71
____ 30. A game-show spinner has 7 equal sections labeled with the colors red, orange, yellow, green, blue, indigo
and violet. What is the probability that on two consecutive spins you get University of Michigan’s colors
(blue and yellow)?
a.
b.
c.
d.
____ 31. Which exponential equation goes through the points (2, 6) and (4, 54)?
a.
y=3
b.
y = 2(3)x
c.
y=
(6)x
d.
y=
(3)x
____ 32. Write a function that models inverse variation if x = 4 when y = −7.
a.
b.
y = −28x
c.
d.
y = 28x
y=
y=
____ 33.
Which graph matches the equation y = −
?
a.
b.
c.
d.
____ 34. What are the asymptotes of the function y =
a.
b.
c.
d.
x = 3, y = 1
x = −5, y = −1
x = −5, y = 3
x = −5, y = 1
?
____ 35. Which of the following graphs best represent the equation y = log8 x?
a.
b.
c.
d.
____ 36. You can use the equation N = k log A to estimate the number of species N that live in a region of area A.
The parameter k is determined by the conditions in the region. In a rain forest, 2700 species live in 500 km2.
How many species would remain if half of the forest area were destroyed by logging and farming?
a.
b.
c.
d.
1595
4567
2641
2399
____ 37. Write this expression in a single logarithm: 2 log x – 4 log y.
a.
b.
____ 38.
log x 2 y 4
log
c.
log (x 2 – y 4)
d.
log (x 2 + y 4)
How is the graph of y = 4 •
a.
b.
c.
d.
translated from the graph of y = 4 •
?
3 units left
3 units right
3 units down
3 units up
____ 39. You roll two six-sided number cubes. What is the probability that at least one of the numbers is even?
a.
b.
c.
d.
____ 40.
Expand the logarithm:
a.
5logb xy + logb 3
b.
5logb x + 5logb y – 5logb 3
c.
5(logb x + logb y) – logb 3
d.
5logb x + logb y – logb 3
.
____ 41. In her first 16 basketball games, Kimberly made 65.8% of her free throws. In the next game, she made 7 of
9 free throws. Let x be the number of free throws Kimberly tried in the first 16 games. What function
represents the percent of free throws made after 17 games?
a.
f(x) =
b.
f(x) =
c.
f(x) =
d.
f(x) =
____ 42. Sound intensity is inversely proportional to the square of the distance from the source—the farther from the
source you are, the less intense the sound. Suppose the sound intensity is 50 watts per square meter at 3
meters. What is the sound intensity at 5 meters?
a.
18 W / m 2
b.
48 W / m 2
c.
30 W / m 2
d.
24 W / m 2
____ 43. Solve the equation log x – log 3 = 2.
a.
b.
c.
d.
300
500
2000
6
____ 44. Write the equation 64 = 1296 in logarithmic form.
a.
log4 6 = 1296
b.
log6 1296 = 4
c.
log1296 6 = 4
d.
log6 4 = 1296
____ 45. Write the equation 100 = 102 in logarithmic form.
a.
log2 10 = 100
b.
c.
log 2 = 100
log2 100 = 10
d.
log 100 = 2
____ 46. Solve the equation e4x = 24.
a.
b.
c.
d.
−6.00
0.34505
6.00000
0.79451
____ 47. Classify this pair of events: You pick one player for your soccer team, then your friend picks a player from
the remaining choices.
a.
b.
independent
dependent
____ 48. Which graph matches the equation y = 2x?
a.
b.
c.
d.
____ 49.
Add and simplify:
a.
b.
c.
d.
+
.
____ 50. Mr. Andersen put $1000 into an account that earns 4.5% annual interest. The interest is compounded
annually and there are no withdrawals. How much money will be in the account at the end of 30 years?
a.
b.
c.
d.
$1300.25
$2051.67
$3745.32
$5431.67
Carefully review your answers on this progress test and make any corrections you feel are necessary. When
you are satisfied that you have answered the questions to the best of your ability, transfer your answers to the
online test submission page in the presence of your proctor.
The University of Nebraska is an equal opportunity educator and employer. ©2018, The Board of Regents of the
University of Nebraska. All rights reserved.

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