Answers Algebra IIExponential and Logarithmic Functions

Exponential and Logarithmic Functions — Test Answers

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Which statement is true?

The second function grows approximately 6 times faster than the first function over the interval 2 is less than x comma x is less than 3 .

The second function grows approximately 21 times slower than the first function over the interval 4 is less than x comma x is less than 5 .

The second function grows approximately 21 times faster than the first function over the interval 4 is less than x comma x is less than 5 .

The second function grows approximately 2 point 5 times slower than the first function over the interval 2 is less than x comma x is less than 3 .

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Which of the following describes the growth rate of the exponential function in the graph?

For each x increase of 1 , the y increases by doubling and then adding 1 .

For each x increase of 1 , the y increases by a common difference of 3 .

For each x increase of 1 , the y increases by 4 more than the previous increase.

For each x increase of 1 , the y increases by a common factor of 3 .

What is the solution to the equation 2 raised to the x plus 4 power minus 12 is equal to 20 ?

x is equal to 1

x is equal to 0

x is equal to 9

x is equal to 2

Which expression is equivalent to the fraction with numerator open paren 6 x to the 5th power z close paren cubed and denominator 4 x to the 4th power z squared ?

the fraction with numerator 3 x to the 4th power z squared and denominator 2

54 x to the 19th power z to the 5th power

the fraction with numerator 9 x to the 11th power z to the th power and denominator 2

54 x to the 11th power z

Which expression is equivalent to open paren 5 x cubed close paren times 4 x cubed ?

8 comma 000 x to the 6th power

500 x to the 6th power

320 x to the 6th power

20 x to the 6th power

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 greater than 0 and b is not equal to 1

b is less than 0 and b is equal to 1

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

For what value of x does 3 raised to the 4 x power is equal to 27 raised to the x minus 3 power ?

negative 3

negative 9

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

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

y is equal to 2 to the x th power

What is the true solution to the equation? the natural log of e raised to the natural log x power plus the natural log of e raised to the the natural log of x squared power is equal to 2 ln 8

x is equal to 2

x is equal to 64

x is equal to 4

x is equal to 8

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 3 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 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 .

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

16 thirds

1 third

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

Which graph represents an exponential decay function?

Image with description On a coordinate plane, the x-axis is labeled 'x' and ranges from negative 10 to 10. The y-axis is labeled 'y' and ranges from negative 10 to 10. A curved line, passes through the points (negative 1 comma 2), (negative 2 comma 4), (negative 3 comma 8), (0 comma 1), (1 comma 0 point 5), and (2 comma 0 point 2 5). The curve has a horizontal asymptote at y equals 0 (the x-axis), which it approaches as x approaches positive infinity.

Image with description On a coordinate plane, the x-axis is labeled 'x' and ranges from negative 10 to 10. The y-axis is labeled 'y' and ranges from negative 10 to 10. A curved line, passes through the points (negative 2 comma 0 point 2 5), (negative 1 comma 0 point 5), (0 comma 1), (1 comma 2), (2 comma 4) and (3 comma 8). The curve has a horizontal asymptote at y equals 0 (the x-axis), which it approaches as x approaches negative infinity.

Image with description On a coordinate plane, the x-axis is labeled 'x' and ranges from negative 10 to 10. The y-axis is labeled 'y' and ranges from negative 10 to 10. A curved line, begins at approximately (0 comma 0) and extends to the right in fourth quadrant. The curve is continuously decreasing and it passes through approximately (1 comma negative 1), (4 comma negative 2), and (9 point 5 comma negative 3).

Image with description On a coordinate plane, the x-axis is labeled 'x' and ranges from negative 10 to 10. The y-axis is labeled 'y' and ranges from negative 10 to 10. A curved line, begins at the origin (0 comma 0) and extends into the first quadrant. The curve is continuously increasing and appears concave down. It passes through (1 comma 1), (3 comma 2), and (8 comma 3).

Calvin deposits 400 dollars in a savings account that accrues 5 percent interest compounded monthly. After c years, Calvin has 658 point 8 0 dollars Makayla deposits 300 dollars in a different savings account that accrues 6 percent interest compounded quarterly. After m years, Makayla has 613 point 0 4 dollars What is the approximate difference in the number of years that Calvin and Makayla have their money invested?

Calvin invests his money 2 years longer.

Makayla invests her money 1 year longer.

Calvin invests his money 1 year longer.

Makayla invests her money 2 years longer.

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

1 fourth

negative 4

negative 1 fourth

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

all real numbers less than 3

all real numbers greater than negative 3

all real numbers greater than 3

all real numbers less than negative 3

A population of insects increases at a rate of 1 point 5 percent per day. About how long will it take the population to double?

2 point 5 days

66 point 7 days

5 point 0 days

46 point 6 days

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

1 point 7 9 6

0 point 5 5 7

0 point 6 2 0

0 point 2 3 3

What is the solution to the given equation? log sub 6 4 x squared minus the log base 6 of x is equal to 2

x is equal to 1 over 12

x is equal to 9

x is equal to 3

x is equal to 3 halves

Which graph shows the solution to the equation? the log base 3 of x is equal to the log base 0 point 5 of x

Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis, both axes labeled from negative 5 to 5 in increments of 1 unit. Four curves are plotted, with two entirely above the x-axis and two entirely below the x-axis. Above the x-axis, one curve extends from an arrow on the y-axis at 0 comma 0.5 up to an upward-pointing arrow near 1 comma 5, and a second curve extends from an upward-pointing arrow near 1 comma 5 down to an arrow near 5 comma 0.5. Below the x-axis, one curve extends from an arrow on the y-axis at 0 comma negative 0.5 down to a downward-pointing arrow near 1 comma negative 5, and a second curve extends from a downward-pointing arrow near 1 comma negative 5 up to an arrow near 5 comma negative 0.5.

Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis, both axes labeled from negative 5 to 5 in increments of 1 unit. A straight line extends from a downward-pointing arrow near negative 5 comma negative 5, passes through 0 comma 0, and continues upward to an arrow near 5 comma 5. A curve extends from a downward-pointing arrow near 0 comma negative 5, increases upward to pass through 1 comma 0, and continues increasing to an arrow near 5 comma 1.5.

Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis, both axes labeled from negative 5 to 5 in increments of 1 unit. Two curves intersect at 1 comma 0. The first curve extends from a downward-pointing arrow near 0 comma negative 5, increases upward to pass through 1 comma 0 and 3 comma 1, and continues increasing to an arrow near 5 comma 1.5. The second curve extends from an upward-pointing arrow near 0 comma 5, decreases downward to pass through 1 comma 0 and 2 comma negative 1, and continues decreasing to an arrow near 5 comma negative 2.5

Image with description On a coordinate plane the x axis lists from negative 5 to 5 by 1 and y axis lists from negative 5 to 5 by 1. There is a curved graph that passes through (negative 4 comma negative 2), and (negative 2 comma negative 1). It increases in the third quadrant, changes direction at the origin, and then again increases in the first quadrant passing through (5 comma 1 point 5). There is line that passes through the origin, (1 comma 1), and (2 comma 2).

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