Answers4328-O Mathematics 3B OnlineUnit Test

Unit Test — Unit test Answers

23 verified answers
1
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The height of a plant over time is shown in the table below. Using a logarithmic model, what is the best estimate for the age of the plant when it is 19 inches tall?Plant Heightt, time in monthsh, height in inches118218.21318.33418.42518.48618.54

A
10 months
B
14 months
C
16 months
D
28 months
2
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A population of insects increases at a rate of 1.5% per day. About how long will it take the population to double?

A
2.5 days
B
5.0 days
C
46.6 days
D
66.7 days
3

Which geometric series converges?

A
StartFraction 1 Over 81 EndFraction + StartFraction 1 Over 27 EndFraction + one-ninth + one-third + ellipsis
Option A
B
1 + one-half + one-fourth + one-eighth + ellipsis
Option B
C
Sigma-Summation Underscript n = 1 Overscript infinity EndScripts 7 (negative 4) Superscript n minus 1
Option C
D
Sigma-Summation Underscript n = 1 Overscript infinity EndScripts one-fifth (2) Superscript n minus 1
Option D
4

Devon purchased a new car valued at $16,000 that depreciated continuously at a rate of 35%. Its current value is $2,000. The equation represents the situation, where t is the age of the car in years and r is the rate of depreciation. About how old is Devon’s car? Use a calculator and round your answer to the nearest whole number.

Question illustration
A
1 year
B
2 years
C
5 years
D
8 years
5

What is the sum of the first seven terms of the geometric series?3 + 12 + 48 + 192 + ...

A
4,372
B
12,288
C
16,383
D
65,535
6

Which equation is represented by the graph below?

Question illustration
A
y = l n x minus 3
Option A
B
y = l n x minus 4
Option B
C
y = e Superscript x Baseline minus 3
Option C
D
y = e Superscript x Baseline minus 4
Option D
7

What is the true solution to the equation below?

Question illustration
A
and
Option A
B
and
Option B
C
and
Option C
D
and
Option D
8

What is the range of the function

Question illustration
A
y less-than 0
Option A
B
y greater-than 0
Option B
C
y less-than 4
Option C
D
y greater-than 4
Option D
9

An equation for the depreciation of a car is given by y = A(1 – r)t , where y = current value of the car, A = original cost, r = rate of depreciation, and t = time, in years. The value of a car is half what it originally cost. The rate of depreciation is 10%. Approximately how old is the car?

A
3.3 years
B
5.0 years
C
5.6 years
D
6.6 years
10

A hospital sends an invoice to a patient. The patient schedules a payment plan in which she makes an initial payment of $1,451 the first month and then pays one-third of the previous month’s payment each of the following months until the invoice is paid in full. Approximately how much of the invoice will be paid after the fourth month?

A
$1,451.00
B
$2,095.89
C
$2,149.63
D
$2,167.54
11

Calvin deposits $400 in a savings account that accrues 5% interest compounded monthly. After c years, Calvin has $658.80. Makayla deposits $300 in a different savings account that accrues 6% interest compounded quarterly. After m years, Makayla has $613.04. What is the approximate difference in the number of years that Calvin and Makayla have their money invested?

A
Makayla invests her money 1 year longer.
B
Makayla invests her money 2 years longer.
C
Calvin invests his money 1 year longer.
D
Calvin invests his money 2 years longer.
12

What is the solution to the equation below?

Question illustration
A
mc008-2.jpg
Option A
B
mc008-3.jpg
Option B
C
mc008-4.jpg
Option C
D
mc008-5.jpg
Option D
13

What is the solution to the equation

Question illustration
A
mc012-2.jpg
Option A
B
mc012-3.jpg
Option B
C
mc012-4.jpg
Option C
D
mc012-5.jpg
Option D
14

What is the range of the function

Question illustration
A
all real numbers less than –1
B
all real numbers greater than –1
C
all real numbers less than 1
D
all real numbers greater than 1
15

A painter is painting a wall with an area of 150 ft2. He decides to paint half of the wall and then take a break. After his break, he paints half of the remaining unpainted portion and then takes another break. If he continues to paint half of the remaining unpainted portion between breaks, approximately what portion of the original wall will be painted when he takes his fifth break?

A
112.50 ft2
B
145.31 ft2
C
147.66 ft2
D
290.63 ft2
16

What is the true solution to the equation below?

Question illustration
A
x = 2
Option A
B
x = 4
Option B
C
x = 8
Option C
D
x = 64
Option D
17

Which of the following shows the graph of

Question illustration
A
On a coordinate plane, a curve starts in quadrant 4 at (0, negative 3) and curves up into quadrant 1 and approaches y = 3. It crosses the x-axis at (1, 0).
Option A
B
On a coordinate plane, a curve approaches the x-axis in quadrant 2 and then increases into quadrant 1. It crosses the y-axis at (0, 4).
Option B
C
On a coordinate plane, a curve approaches the x-axis in quadrant 2 and then increases into quadrant 1. It crosses the y-axis at (0, 2).
Option C
D
On a coordinate plane, a curve approaches the y-axis in quadrant 4 and then increases into quadrant 1 and approaches y = 5. It crosses the x-axis at (1, 0).
Option D
18

What common base can be used to rewrite each side of the equation

Question illustration
A
2
B
3
C
5
D
8
19

The equation for the pH of a substance is pH = –log[H+], where H+ is the concentration of hydrogen ions. Which equation models the concentration of hydrogen ions (H+) of a solution whose pH is 7.2?

A
[H+] = log7.2
B
[H+] = -log7.2
C
[H+] =
Option C
D
[H+] =
Option D
20

Two students start a club the first week of school. Each member invites three new members the second week of school. Each of these new members then invites three additional members the following week. If the pattern of each new member inviting three new members each week continues, how many members will be in the club after five weeks?

A
80 students
B
121 students
C
242 students
D
363 students

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