AnswersAlgebra IIExponential and Logarithmic Functions

Practice Test Answers

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Which rule can be used to describe the growth of the y -values of the function y is equal to 12 to the x th power over each interval from x is equal to negative 1 to x is equal to 3 ?

A
add 12
B
multiply by 12
C
add 1 , then 12 , then 144
D
multiply by 1 , then by 12 , then by 144
2
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Which expression is equivalent to the fraction with numerator 15 A to the 8th power b to the 4th power and denominator 5 A to the 4th power b ?

A
10 A to the 4th power b to the 4th power
B
3 A to the 4th power b cubed
C
3 A squared b to the 4th power
D
10 A to the 4th power b cubed
3

If 343 to the x th power is equal to 49 raised to the 4 minus x power , what is the value of x ?

A
8
B
5 eighths
C
8 fifths
D
2
4

One brand of vinegar has a pH of 4 point 5 Another brand has a pH of 5 point 0 The equation for the pH of a substance is pH is equal to negative log times open bracket cap h raised to the plus power close bracket , 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?

A
2 point 2 times 10 to the negative 5 power
B
6 point 8 times 10 to the 4th power
C
3 point 2 times 10 to the 1th power
D
3 point 2 times 10 inverse
5

Two different radioactive isotopes decay to 10 percent 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?

A
33 days
B
10 days
C
3 days
D
13 days
6

What are the domain and range of f of x is equal to the log of open paren x minus 1 close paren plus 2 ?

A
domain : all real numbers; range: y is greater than 1
B
domain: x is greater than 1 ; range: all real numbers
C
domain: all real numbers; range: all real numbers
D
domain: x is greater than 1 ; range: y is greater than 2
7

Which function has a horizontal asymptote of y is equal to 3 ?

A
f of x is equal to 3 times open paren 2 to the x th power close paren
B
f of x is equal to 2 times open paren 4 to the x th power close paren plus 3
C
f of x is equal to 2 times open paren 3 to the x th power close paren
D
f of x is equal to 2 times 4 raised to the x minus 3 power
8

What is the solution of the log base x of 729 is equal to 3 ?

A
18
B
6
C
81
D
9
9

Which of the following shows the graph of y is equal to the natural log of open paren negative 2 x close paren ?

A
Image with description On a coordinate plane, the x and y axis ranges from negative 5 to 5 with increment of 1. There is a curved graph that starts from the quadrant II, crosses the x axis at 0 point 5 comma 0, decreases with the increased value of x. It approaches y axis in the quadrant III.
B
Image with description On a coordinate plane, the x and y axis ranges from negative 5 to 5 with increment of 1. There is a curved graph that starts from the quadrant I, crosses the x axis at 0 point 5 comma 0, decreases with x value. It approaches y axis in the quadrant IV.
C
Image with description On a coordinate plane, the x and y axis ranges from negative 5 to 5 with increment of 1. There is a curved graph that starts from the quadrant I, crosses the x axis at point 4 comma 0, decreases with x value. It approaches y axis in the quadrant IV.
D
Image with description On a coordinate plane, the x and y axis ranges from negative 5 to 5 with increment of 1. There is a curved graph that starts from the quadrant II, crosses the x axis at point negative 4 comma 0, decreases with the increased value of x. It approaches y axis in the quadrant III.
10

The two expressions have the same value when rounded to the nearest hundredth. the log base 5 of b the log base 9 of 48 What is the approximate value of log b to the nearest hundredth?

A
65 point 5 3
B
1 point 2 3
C
0 point 9 3
D
9 point 1 6
11

Which expression is equivalent to c d to the 5th power ?

A
c to the 5th power plus d to the 5th power
B
the fraction with numerator c to the 5th power and denominator d to the 5th power
C
c to the 5th power minus d to the 5th power
D
c to the 5th power d to the 5th power
12

What is the solution of the natural log of open paren x plus 6 close paren minus natural log 9 is equal to 2 ? Round your answer to the nearest hundredth.

A
x is equal to 72 point 5 0
B
x is equal to 60 point 5 0
C
x is equal to 66 point 5 0
D
x is equal to 53 point 5 0
13

What is the range of y is equal to log sub 2 of open paren x minus 6 close paren ?

A
all real numbers less than 6
B
all real numbers not equal to 0
C
all real number greater than 6
D
all real numbers
14

For what value of x does 625 is equal to 5 raised to the 6 minus 2 x power ?

A
4
B
1
C
2
D
5
15

The intensity, or loudness, of a sound can be measured in decibels d cap b , according to the equation cap i times d cap b is equal to 10 log open bracket the fraction with numerator cap i and denominator cap i sub 0 close bracket , where cap i is the intensity of a given sound and cap i sub 0 is the threshold of hearing intensity. What is the intensity, in decibels, open bracket cap i times d cap b close bracket , when cap i is equal to 10 to the 32th power times open paren cap i sub 0 close paren ?

A
320
B
15
C
737
D
32
16

What is the range of the function f of x is equal to negative 2 times open paren 6 to the x th power close paren plus 3 ?

A
open paren negative infinity comma 3 close paren
B
left bracket negative 2 comma infinity right parenthesis
C
left bracket 3 comma infinity right parenthesis
D
left parenthesis negative infinity comma negative 2 right bracket
17

What is the domain of the function y is equal to the natural log of open paren x plus 2 close paren ?

A
x is less than 2
B
x is greater than negative 2
C
x is less than negative 2
D
x is greater than 2
18

Which graph shows the solution to the equation? log sub 3 of open paren x plus 2 close paren is equal to 1

A
Image with description On a coordinate plane the x axis lists from negative 3 to 9 by 1 and y axis lists from negative 4 to 8 by 1. There is a smooth curve that approaches the line x equals negative 2 in the third quadrant. It passes through the point (negative 1 comma 0), (8 comma 1) and increases as x increases. There is a line that is parallel to the x axis and cuts the y axis at (0 comma 1).
B
Image with description Coordinate plane with x-axis and y-axis. A logarithmic-shaped curve begins near the y-axis at x equals 0 and extends to the right. The curve passes through 1 comma 0, rises gradually through approximately 3 comma 1 and 9 comma 2, and continues increasing as x increases. A horizontal line y equals negative 1 extends across the graph with arrows on both ends. The curve intersects the horizontal line near 0.3 comma negative 1 and lies above the line for x values greater than this point. Both the curve and the horizontal line continue indefinitely as indicated by arrows.
C
Image with description On a coordinate plane the x axis lists from negative 3 to 9 by 1 and y axis lists from negative 4 to 8 by 1. There is a smooth curve that approaches the line x equals negative 2 in the third quadrant. It passes through the point (negative 1 comma 0), (8 comma 1) and increases as x increases. There is a line that is parallel to the x axis and cuts the y axis at (0 comma negative 1).
D
Image with description On a coordinate plane the x axis lists from negative 3 to 9 by 1 and y axis lists from negative 4 to 8 by 1. There is a smooth curve that approaches the line x equals negative 2 in the third quadrant. It passes through the point (negative 1 comma 0), (1 comma 1) and increases as x increases. There is a line parallel to the x axis and cuts the y axis at (0 comma 1).
20

Which statement is true about the functions?

A
The linear function is generally growing faster than the exponential function.
B
The exponential function and the linear function are generally growing at the same rate.
C
The exponential function is generally growing slower than the linear function.
D
The exponential function is generally growing faster than the linear function.

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