Answers LAUSD-Algebra II B Prescriptive - SummerModeling with Exponential and Logarithmic Equations

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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?

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What is the domain of the function

x less-than negative 2

x greater-than negative 2

x less-than 2

x greater-than 2

What are the domain and range of ?

domain: x > 1; range: y > 2

domain: x > 1; range: all real numbers

domain: all real numbers; range: y > 1

domain: all real numbers; range: all real numbers

What is the range of ?

all real numbers not equal to 0

all real numbers less than 6

all real number greater than 6

all real numbers

What is written as a single logarithm?

4 log Subscript one-half Baseline 2 Superscript 4 Baseline u squared minus v cubed

log Subscript one-half Baseline w Superscript 4 Baseline (StartFraction u squared Over v cubed EndFraction)

log Subscript one-half Baseline (StartFraction w Superscript 4 Baseline Over u squared v cubed EndFraction)

log Subscript one-half Baseline (w (StartFraction u squared Over v cubed EndFraction)) Superscript 4

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?

step 1

step 2

step 3

step 4

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

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

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).

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

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

Jerome solved the equation below by graphing.Which of the following shows the correct system of equations and solution?

; x = 3

; x = 4

; x = 33

; x = 44

Which of the following shows the graph of y = –(2)x – 1?

On a coordinate plane, a curve is level at y = 0 in quadrant 2 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, negative 0.5).

On a coordinate plane, a curve is level at y = negative 1 in quadrant 3 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, negative 2).

On a coordinate plane, a curve is level at y = 1 in quadrant 3 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, 0).

On a coordinate plane, a curve is level at y = 0 in quadrant 2 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, negative 2).

What is the range of the function f(x) = –2(6x) + 3?

(negative infinity, negative 2 Right-bracket

(negative infinity, 3)

Left-bracket negative 2, infinity)

Left-bracket 3, infinity)

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 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

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.

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.

Which expression is equivalent to ?

log Subscript 2 Baseline 9 + 3 log Subscript 2 Baseline x

log Subscript 2 Baseline x + 3 log Subscript 2 Baseline 9

3 log Subscript 2 Baseline x minus log Subscript 2 Baseline 9

3 log Subscript 2 Baseline 9 minus log Subscript 2 Baseline x

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

What is the range of the function graphed below?

y greater-than 0

y less-than 0

y greater-than 0

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).

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

The magnitude, M, of an earthquake is defined to be , where I is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and S is the intensity of a “standard” earthquake, which is barely detectable. What is the magnitude of an earthquake that is 1,000 times more intense than a standard earthquake? Use a calculator. Round your answer to the nearest tenth.

4.5

6.9

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