Answers Algebra IIExponential and Logarithmic Functions

Exponential and Logarithmic Functions — Test Answers

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Which graph represents an exponential decay function?

Image with description On a coordinate plane, the curve passes through (negative 3 comma 8), (negative 2 comma 4), (negative 1 comma 2), and (0 comma 1). It approaches to the x-axis as the value of x increases.

Image with description On a coordinate plane, the curve passes through (0 comma 1), (1 comma 2), (2 comma 4), and (3 comma 8). It approaches to the x-axis as the value of x decreases.

Image with description On a coordinate plane, the curve originate on y-axis and passes through (1 comma 1), (4 comma 2),and (8 comma 3) in the first quadrant.

Image with description On a coordinate plane, the curve originate on y-axis and passes through (1 comma negative 1) and (4 comma negative 2) in the fourth quadrant.

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The range of which function is open paren 2 comma infinity close paren ?

y is equal to 2 to the x th power

y is equal to 5 to the x th power plus 2

y is equal to 2 times open paren 5 to the x th power close paren

y is equal to 5 raised to the x plus 2 power

What is the domain of y is equal to log sub 4 of open paren x plus 3 close paren ?

all real numbers greater than 3

all real numbers less than 3

all real numbers greater than negative 3

all real numbers less than negative 3

What is the value of the log base 625 of 5 ?

1 fourth

negative 4

negative 1 fourth

The equation cap t squared is equal to cap A cubed shows the relationship between a planet’s orbital period, cap t , and the planet’s mean distance from the sun, cap A , in astronomical units, AU. If the orbital period of planet Y is twice the orbital period of planet X, by what factor is the mean distance increased?

2 raised to the 1 third power

2 raised to the 2 thirds power

2 raised to the 1 half power

2 raised to the 3 halves power

What is the approximate value of the log base 6 of 25 ?

0 point 5 5 7

0 point 2 3 3

0 point 6 2 0

1 point 7 9 6

Which of the following shows the extraneous solution to the logarithmic equation? log sub 3 of open paren 18 x cubed close paren minus log sub 3 of 2 x is equal to the log base 3 of 144

x is equal to negative 4

x is equal to negative 8

x is equal to negative 2

x is equal to negative 16

How does the value of log_2⁡100 compare with the value of the log base 6 of 20 ?

The value of the log base 2 of 100 is about 4 times the value of the log base 6 of 20 .

The value of the log base 2 of 100 is about 1 third times the value of the log base 6 of 20 .

The value of the log base 2 of 100 is about 1 fourth times the value of the log base 6 of 20 .

The value of the log base 2 of 100 is about 3 times the value of the log base 6 of 20 .

The magnitude, cap m , of an earthquake is defined to be cap m is equal to the log of cap i over cap s , where cap i is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and cap 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.

negative 0 point 5

1 point 5

3 point 6

negative 1 point 5

What is the solution to log sub 5 of open paren x plus 30 close paren is equal to 3 ?

x is equal to negative 95

x is equal to 5

x is equal to negative 5

x is equal to 95

If you are given the graph of h of x is equal to the log base 6 of x , how could you graph m times x is equal to log sub 6 of open paren x plus 3 close paren ?

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

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

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

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

For what value of n does the fraction with numerator 216 raised to the n minus 2 power and denominator open paren 1 over 36 close paren raised to the 3 n power is equal to 216 ?

negative 3

5 ninths

negative 1 third

Which expression is equivalent to 144 raised to the 3 halves power ?

cube root of 72

1 comma 728

216

cube root of 12

For what value of n does open paren 1 over 36 close paren to the n th power is equal to 216 ?

3 halves

negative 3

negative 3 halves

What is the solution of log sub 2 of open paren 3 x minus 7 close paren is equal to 3 ?

1 third

16 thirds

Which is the graph of y is equal to the log of negative x ?

Image with description On a coordinate plane, the x-axis lists negative 9 to 3 by 1, and the y-axis lists negative 5 to 5 by 1. The graph has a curve that originates from (0 comma 3 point 5), goes down and intersects the x-axis at (negative 1 comma 0). It passes through (negative3 comma negative 1) and (negative 7 comma negative 2).

Image with description On a coordinate plane, the x-axis lists negative 10 to 4 by 1, and the y-axis lists negative 6 to 6 by 1. The curve has a curve that originates from (0 comma negative 1 point 5). It intersects the x-axis at (negative 1 comma 0) and goes through (negative 8 comma 1).

Image with description On a coordinate plane, the x-axis lists negative 4 to 10 by 1, and the y-axis lists negative 5 to 5 by 1. The graph has a curve that originates from (0 comma negative 3). It intersects the x-axis at (1 comma 0), and goes through (7 comma 2).

Which of the following shows the graph of y is equal to 4 to the x th power plus 3 ?

Image with description On a coordinate plane, the curve passes through (3 comma 1) and (4 comma 4).It increases rapidly in the first quadrant as x increase and goes towards line y equal 0 as x decreases in the second quadrant.

Image with description On a coordinate plane, the curve passes through (negative 3 comma 1) and (negative 2 comma 4).It increases rapidly in the first quadrant as x increase and goes towards line y equal 0 as x decreases in the second quadrant.

Image with description On a coordinate plane, the curve passes through (0 comma 4) and (1 comma 7).It increases rapidly in the first quadrant as x increase and goes towards line y equal 3 as x decreases in the second quadrant.

Image with description On a coordinate plane, the curve passes through (0 comma negative 2) and (1 comma 1).It increases rapidly in the first quadrant as x increase and goes towards line y equal negative 3 as x decreases in the third quadrant.

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

b is greater than 0 and b is equal to 1

b is less than 0 and b is not equal to 1

b is less than 0 and b is equal to 1

b is greater than 0 and b is not equal to 1

Mario invested 6 dollars comma 000 in an account that pays 5 percent annual interest compounded annually. Using the formula cap A is equal to cap p times open paren 1 plus r close paren to the t th power , what is the approximate value of the account after 2 point 5 years?

6 dollars comma 778

6 dollars comma 118

6 dollars comma 456

6 dollars comma 075

Which expression is equivalent to open paren 64 y to the 100th power close paren raised to the 1 half power ?

8 y to the 10th power

32 y to the 50th power

32 y to the 10th power

8 y to the 50th power

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Exponential and Logarithmic Functions — Test Answers

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