AnswersPBCSD_Grade_Forgiveness_1200330_Algebra 2_S2_2024Base e

Base e — Unit test Answers

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1
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Which function is shown in the graph below?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
2
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Which of the following shows the graph of y = –(2)x – 1?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
3

If , what is the value of x?

Question illustration
A
Five-eighths
Option A
B
Eight-fifths
Option B
C
2
D
8
4

Which equation has x = 4 as the solution?

A
log Subscript 4 Baseline (3 x + 4) = 2
Option A
B
log Subscript 3 Baseline (2 x minus 5) = 2
Option B
C
log Subscript x Baseline 64 = 4
Option C
D
log Subscript x Baseline 16 = 4
Option D
5

Two different radioactive isotopes decay to 10% of their respective original amounts. Isotope A does this in 33 days, while isotope B does this in 43 days. What is the approximate difference in the half-lives of the isotopes?

A
3 days
B
10 days
C
13 days
D
33 days
6

Which function has a horizontal asymptote of y = 3?

f
f(x) = 3(2x)
f
f(x) = 2(4)x–3
f
f(x) = 2(3x)
f
f(x) = 2(4x) + 3
7

A student showed the steps below while solving the equation by graphing.Step 1:Write a system of equations: Step 2: Use the change of base formula to rewrite the equations:Step 3:Graph the two equations:Step 4:Identify the x-value at the point of intersection:In which step did the student make the first error?

Question illustration
A
step 1
B
step 2
C
step 3
D
step 4
8

Which of the following shows the graph of

Question illustration
A
On a coordinate plane, a curve approaches the y-axis in quadrant 3. It increases into quadrant 2 and crosses the x-axis at (negative 0.5, 0).
Option A
B
On a coordinate plane, a curve approaches the y-axis in quadrant 3. It increases into quadrant 2 and crosses the x-axis at (negative 4, 0).
Option B
C
On a coordinate plane, a curve approaches the y-axis in quadrant 4. It increases into quadrant 1 and crosses the x-axis at (0.5, 0).
Option C
D
On a coordinate plane, a curve approaches the y-axis in quadrant 4. It increases into quadrant 1 and crosses the x-axis at (4, 0).
Option D
9

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

Question illustration
T
Translate each point of the graph of g(x) 5 units up.
T
Translate each point of the graph of g(x) 5 units down.
T
Translate each point of the graph of g(x) 5 units left.
T
Translate each point of the graph of g(x) 5 units right.
10

What is the range of the function graphed below?

Question illustration
A
y greater-than 0
Option A
B
y less-than 0
Option B
C
y less-than 0
Option C
D
y greater-than 0
Option D
11

Which graph shows the solution to the equation below?

Question illustration
A
On a coordinate plane, a curve starts in quadrant 3 and curves up into quadrant 1 and approaches y = 3. It crosses the x-axis at (1, 0). A horizontal straight line is at y = 1.
Option A
B
On a coordinate plane, a curves starts in quadrant 4 and curves up into quadrant 1 and approaches y = 3. It crosses the x-axis at (1, 0). A horizontal straight line is at y = negative 1.
Option B
C
On a coordinate plane, a curve starts in quadrant 3 and curves up into quadrant 1 and approaches y = 1. It crosses the x-axis at (negative 1, 0). A horizontal straight line is at y = 1.
Option C
D
On a coordinate plane, a curves starts in quadrant 3 and curves up into quadrant 1 and approaches y = 2. It crosses the x-axis at (negative 1, 0). A horizontal straight line is at y = negative 1.
Option D
12

One brand of vinegar has a pH of 4.5. Another brand has a pH of 5.0. The equation for the pH of a substance is pH = –log[H+], where H+ is the concentration of hydrogen ions. What is the approximate difference in the concentration of hydrogen ions between the two brands of vinegar?

A
mc017-1.jpg
Option A
B
mc017-2.jpg
Option B
C
mc017-3.jpg
Option C
D
mc017-4.jpg
Option D
13

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 current value of a car is $12,282.50. The car originally cost $20,000 and depreciates at a rate of 15% per year. How old is the car?

A
years
Option A
B
years
Option B
C
3 years
D
4 years
14

Two different cars each depreciate to 60% of their respective original values. The first car depreciates at an annual rate of 10%. The second car depreciates at an annual rate of 15%. What is the approximate difference in the ages of the two cars?

A
1.7 years
B
2.0 years
C
3.1 years
D
5.0 years
15

Which is the graph of ?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D

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