Answers 00TX-Algebra II B-CRSolving Exponential and Logarithmic Equations

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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

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What is the solution to the equation

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What is the true solution to the equation below?

x = 2

x = 4

x = 8

x = 64

A function is graphed on a coordinate grid. As the domain values approach infinity, the range values approach infinity. As the domain values approach negative infinity, the range values approach infinity. To which family of functions might the described function belong?

reciprocal

square root

exponential

quadratic

The graph of is transformed as shown in the graph below. Which equation represents the transformed function?

y = x cubed minus 4

y = (x minus 4) cubed

y = (negative x minus 4) cubed

y = (negative x) cubed minus 4

What is the true solution to the equation below?

and

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

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)

Based on the family the graph below belongs to, which equation could represent the graph?

y = StartFraction 1 Over x + 2 EndFraction + 3

y = 0.2 Superscript x Baseline + 3

y = x cubed + 3

y = log x + 3

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

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

How is the graph of transformed to produce the graph of ?

The graph is translated left 5 units, compressed vertically by a factor of , and translated up 3 units.

The graph is stretched vertically by a factor of , translated left 5 units, and translated up 3 units.

The graph is translated left 5 units, compressed horizontally by a factor of , and translated down 3 units.

The graph is stretched horizontally by a factor of , translated left 5 units, and translated down 3 units.

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