AnswersCR - Algebra 2 26-27 - S2Solving Logarithmic Equations using Technology

Solving Logarithmic Equations using Technology — Unit test Answers

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How does the value of compare with the value of ?

Question illustration
A
The value of is about 4 times the value of .
Option A
B
The value of is about times the value of .
Option B
C
The value of is about 3 times the value of .
Option C
D
The value of is about times the value of .
Option D
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

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.
4

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
5

Which graph represents an exponential decay function?

A
On a coordinate plane, a curve opens up and to the right in quadrant 4.
Option A
B
On a coordinate plane, a curve opens up and to the right in quadrants 1 and 2. The line rapidly decreases in quadrant 2 and then curves and approaches the x-axis in quadrant 1.
Option B
C
On a coordinate plane, a line slightly curves up in quadrant 1.
Option C
D
On a coordinate plane, a line slowly increases in quadrant 2 and then increases rapidly into quadrant 1.
Option D
6

A radioactive element has a half-life of six days. What is the approximate decay rate of the element after the first day?

A
0.9%
B
1.5%
C
8.3%
D
10.9%
7

Which graph shows the solution to the equation below?

Question illustration
A
On a coordinate plane, 2 curves intersect at (1, 0).
Option A
B
On a coordinate plane, a line intersects with a curve.
Option B
C
On a coordinate plane, a line with positive slope and a curve are shown.
Option C
D
On a coordinate plane, 2 hyperbolas are shown.
Option D
8

What is the domain of ?

Question illustration
A
all real numbers less than –3
B
all real numbers greater than –3
C
all real numbers less than 3
D
all real numbers greater than 3
9

Which of the following shows the graph of y = 4x + 3?

A
On a coordinate plane, an exponential function starts at y = 3 in quadrant 2 and then increases rapidly into quadrant 1.
Option A
B
On a coordinate plane, an exponential function starts at y = 0 in quadrant 2 and then increases rapidly in quadrant 2.
Option B
C
On a coordinate plane, an exponential function starts at y = 0 in quadrant 2 and then increases rapidly into quadrant 1.
Option C
D
On a coordinate plane, an exponential function starts at y = negative 3 in quadrant 3 and then increases rapidly into quadrant 1.
Option D
10

For what value of n does ?

Question illustration
A
–3
B
Negative three-halves
Option B
C
Three-halves
Option C
D
3
11

Which is the graph of ?

Question illustration
A
On a coordinate plane, a curve starts at y = negative 3 and curves up into quadrant 1. It approaches y = 3.
Option A
B
On a coordinate plane, a curve starts at y = negative 2 and curves up into quadrant 2. It approaches y = 2 in quadrant 2.
Option B
C
On a coordinate plane, a curve starts at y = 3 and curves down into quadrant 4. It approaches y = negative 3 in quadrant 4.
Option C
D
On a coordinate plane, a curve starts at y = 4 and curves down into quadrant 3. It approaches y = negative 3 in quadrant 3.
Option D
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

If , what is the value of s?

Question illustration
A
–1
B
0
C
1
D
no solution
14

The population, p, of a town after t years is represented using the equation . Which of the following is an equivalent expression?

Question illustration
A
mc005-2.jpg
Option A
B
mc005-3.jpg
Option B
C
mc005-4.jpg
Option C
D
mc005-5.jpg
Option D
15

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
16

Which of the following is true about the base b of a logarithmic function?

A
b > 0 and b = 1
B
b > 0 and
Option B
C
b < 0 and
Option C
D
b < 0 and b = 1
17

If you are given the graph of , how could you graph ?

Question illustration
A
Translate each point of the graph of h(x) 3 units up.
B
Translate each point of the graph of h(x) 3 units down.
C
Translate each point of the graph of h(x) 3 units right.
D
Translate each point of the graph of h(x) 3 units left.
18

If the equation below is solved by graphing, which statement is true?

Question illustration
A
The curves intersect at approximately x = 0.46.
B
The curves intersect at approximately x = 0.75.
C
The curves intersect at approximately x = 1.11.
D
The curves intersect at approximately x = 3.07.
19

The range of which function is ?

Question illustration
A
y = 2x
B
y = 2(5x)
C
y = 5x +2
D
y = 5x + 2
20

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

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Solving Logarithmic Equations using Technology