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

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

The curves intersect at approximately x = 0.46.

The curves intersect at approximately x = 0.75.

The curves intersect at approximately x = 1.11.

The curves intersect at approximately x = 3.07.

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

Translate each point of the graph of h(x) 3 units up.

Translate each point of the graph of h(x) 3 units down.

Translate each point of the graph of h(x) 3 units right.

Translate each point of the graph of h(x) 3 units left.

Which function is shown in the graph below?

y = (one-half) Superscript x + 3 Baseline minus 1

y = (one-half) Superscript x minus 3 Baseline + 1

y = (one-half) Superscript x minus 1 Baseline + 3

y = (one-half) Superscript x + 1 Baseline minus 3

Which is the graph of ?

On a coordinate plane, a curve starts at y = negative 3 and curves up into quadrant 1. It approaches y = 3.

On a coordinate plane, a curve starts at y = negative 2 and curves up into quadrant 2. It approaches y = 2 in quadrant 2.

On a coordinate plane, a curve starts at y = 3 and curves down into quadrant 4. It approaches y = negative 3 in quadrant 4.

On a coordinate plane, a curve starts at y = 4 and curves down into quadrant 3. It approaches y = negative 3 in quadrant 3.

How does the value of compare with the value of ?

The value of is about 4 times the value of .

The value of is about times the value of .

The value of is about 3 times the value of .

The value of is about times the value of .

The range of which function is ?

y = 2x

y = 2(5x)

y = 5x +2

y = 5x + 2

What is the range of the function

all real numbers less than –1

all real numbers greater than –1

all real numbers less than 1

all real numbers greater than 1

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 35 times more intense than a standard earthquake? Use a calculator. Round your answer to the nearest tenth.

–1.5

–0.5

1.5

3.6

The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as , where and is the least intense sound a human ear can hear. What is the approximate loudness of a rock concert with a sound intensity of 10–1?

2 Db

22 Db

60 Db

110 Db

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?

Makayla invests her money 1 year longer.

Makayla invests her money 2 years longer.

Calvin invests his money 1 year longer.

Calvin invests his money 2 years longer.

Which equation is represented by the graph below?

y = l n x minus 3

y = l n x minus 4

y = e Superscript x Baseline minus 3

y = e Superscript x Baseline minus 4

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

10 months

14 months

16 months

28 months

Which graph represents an exponential decay function?

On a coordinate plane, a curve opens up and to the right in quadrant 4.

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.

On a coordinate plane, a line slightly curves up in quadrant 1.

On a coordinate plane, a line slowly increases in quadrant 2 and then increases rapidly into quadrant 1.

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

On a coordinate plane, an exponential function starts at y = 3 in quadrant 2 and then increases rapidly into quadrant 1.

On a coordinate plane, an exponential function starts at y = 0 in quadrant 2 and then increases rapidly in quadrant 2.

On a coordinate plane, an exponential function starts at y = 0 in quadrant 2 and then increases rapidly into quadrant 1.

On a coordinate plane, an exponential function starts at y = negative 3 in quadrant 3 and then increases rapidly into quadrant 1.

What is the domain of the function graphed below?

mc023-2.jpg

mc023-3.jpg

mc023-4.jpg

mc023-5.jpg

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 is the threshold of hearing intensity. What is the intensity, in decibels, [I(dB)], when ?

What is the solution to the equation

mc012-2.jpg

mc012-3.jpg

mc012-4.jpg

mc012-5.jpg

The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as , where and is the least intense sound a human ear can hear. Jessica is listening to soft music at a sound intensity level of 10-9 on her computer while she does her homework. Braylee is completing her homework while listening to very loud music at a sound intensity level of 10-3 on her headphones. How many times louder is Braylee’s music than Jessica’s?

times louder

3 times louder

30 times louder

90 times louder

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

b > 0 and b = 1

b > 0 and

b < 0 and

b < 0 and b = 1

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.

1 year

2 years

5 years

8 years

What is the solution to the equation below?

mc008-2.jpg

mc008-3.jpg

mc008-4.jpg

mc008-5.jpg

What is the approximate value of ?

0.233

0.557

0.620

1.796

What are the domain and range of the step function below?

domain = {all real numbers}, range = {all real numbers}

domain = {all real numbers}, range = {...–4, –1, 2, 5, ...}

domain = {...–5, –2, 1, 4, ...}, range = {...–4, –1, 2, 5, ...}

domain = {all integers}, range = {all real numbers}

The equation of the piecewise defined function f(x) is below. What is the value of f(1)?

f(1) = –2

f(1) = –1

f(1) = 2

f(1) = 3

Which expression is equivalent to ?

4 log Subscript 12 Baseline x + one-half log Subscript 12 Baseline (x cubed minus 2) minus 5 log Subscript 12 Baseline (x times 1)

4 log Subscript 12 Baseline x + one-half log Subscript 12 Baseline StartFraction x cubed Over 2 EndFraction minus 5 log Subscript 12 Baseline 1

log Subscript 12 Baseline 4 x + one-half log Subscript 12 Baseline (x cubed minus 2) minus 5 log Subscript 12 Baseline (x) + 1

4 log Subscript 12 Baseline x + one-half log Subscript 12 Baseline (x cubed minus 2) minus 5 log Subscript 12 Baseline (x + 1)

What is the range of the function

y less-than 0

y greater-than 0

y less-than 4

y greater-than 4

A city manager made the graph below to represent the number of passengers that city buses can carry, where the number of passengers is represented by x, and the number of buses by y.If all city buses carry the same number of passengers, what is the least number of buses needed to carry 710 passengers?