Answers AZ-Common Core Algebra II BUnit Test

Unit Test — Unit test Answers

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Which function has a horizontal asymptote of y = 3?

f(x) = 3(2x)

f(x) = 2(4)x–3

f(x) = 2(3x)

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

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Identify the equation that translates five units down.

y = l n (x minus 5)

y = l n (x) + 5

y = l n (x + 5)

y = l n (x) minus 5

What is the solution of Round your answer to the nearest hundredth.

Option

The two expressions below have the same value when rounded to the nearest hundredth.What is the approximate value of to the nearest hundredth?

0.93

1.23

9.16

65.53

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?

3 days

10 days

13 days

33 days

The intensity, or loudness, of a sound can be measured in decibels (dB), according to the equation , where I is the intensity of a given sound and I0 is the threshold of hearing intensity. What is the intensity, in decibels, [I(dB)], when ?

320

737

An initial investment of $200 is now valued at $350. The annual interest rate is 8% compounded continuously. The equation represents the situation, where t is the number of years the money has been invested. About how long has the money been invested? Use a calculator and round your answer to the nearest whole number.

5 years

7 years

19 years

22 years

Adita has two options for how to invest $1,000.Plan A: Put the $1,000 in an account that pays $100 per year.Plan B: Put the $1,000 in an account that pays 5 percent interest per year.Which statement is true?

Plan A will be worth more than plan B after two years.

Plan A will be worth the same amount as plan B after one year.

Plan B will be worth more than plan A after three years.

Plan B will be worth more than plan A after four years.

A scientist writes the equation to model the growth of a certain bacteria in a petri dish, where N represents the number of bacteria after h hours. After approximately how many hours will 450 bacteria be present? Round your answer to the nearest whole number.

1 hour

6 hours

13 hours

15 hours

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?

Option

Which is the graph of ?

On a coordinate plane, a curve starts at (2, 0) and curves up and goes through (3, 3) and (9, 5).

Option

On a coordinate plane, a curve starts at (2, 6) and curves down and goes through (3, 3) and (10, 2).

Which graph shows the solution to the equation below?

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.

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.

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.

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.

Which equation has x = 4 as the solution?

log Subscript 4 Baseline (3 x + 4) = 2

log Subscript 3 Baseline (2 x minus 5) = 2

log Subscript x Baseline 64 = 4

log Subscript x Baseline 16 = 4

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?

1.7 years

2.0 years

3.1 years

5.0 years

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?

years

3 years

4 years

Which of the following shows the graph of

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).

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).

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).

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).

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

Translate each point of the graph of g(x) 5 units up.

Translate each point of the graph of g(x) 5 units down.

Translate each point of the graph of g(x) 5 units left.

Translate each point of the graph of g(x) 5 units right.

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?