AnswersMathematics IIIMathematical Modeling: Part Two

Mathematical Modeling: Part Two — Test Answers

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1
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Which function is shown in the graph?

A
y is equal to 1 half raised to the x plus 3 power minus 1
B
y is equal to 1 half raised to the x minus 3 power plus 1
C
y is equal to 1 half raised to the x minus 1 power plus 3
D
y is equal to 1 half raised to the x plus 1 power minus 3
2
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Which equation is represented by the graph?

A
y is equal to e to the x th power minus 3
B
y is equal to e to the x th power minus 4
C
y is equal to natural log x minus 3
D
y is equal to natural log x minus 4
3

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

A
x is equal to 9
B
x is equal to 0
C
x is equal to 1
D
x is equal to 2
4

Which expression is equivalent to open paren 5 to the negative 2 power close paren times open paren 5 inverse close paren ?

A
negative 1 over 125
B
1 over 125
C
1 fifth
D
negative 1 fifth
5

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

A
negative 3
B
3
C
3 halves
D
negative 3 halves
6

Which expression is equivalent to log sub w the fraction with numerator open paren x squared minus 6 close paren to the 4th power and denominator cube root of x squared plus 8 ?

A
4 log sub w open paren x squared minus 6 close paren minus 3 log sub w open paren x squared plus 8 close paren
B
4 times open paren log sub w x squared minus 1 third log sub w open paren x squared plus 8 close paren minus 6 close paren
C
4 log sub w the fraction with numerator x squared and denominator 1296 minus 1 third log sub w open paren 2 x plus 8 close paren
D
4 log sub w open paren x squared minus 6 close paren minus 1 third log sub w open paren x squared plus 8 close paren
7

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

A
x is equal to 5
B
x is equal to negative 5
C
x is equal to negative 95
D
x is equal to 95
8

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

A
b is less than 0 and b is not equal to 1
B
b is less than 0 and b is equal to 1
C
b is greater than 0 and b is equal to 1
D
b is greater than 0 and b is not equal to 1
9

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

A
all real numbers less than negative 3
B
all real numbers greater than negative 3
C
all real numbers greater than 3
D
all real numbers less than 3
10

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

A
x is equal to 64
B
x is equal to 8
C
x is equal to 2
D
x is equal to 4
11

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

A
negative 1 fourth
B
4
C
1 fourth
D
negative 4
12

Which expression is equivalent to log sub 12 the fraction with numerator x to the 4th power square root of x cubed minus 2 end root and denominator open paren x plus 1 close paren to the 5th power ?

A
4 log sub 12 x plus 1 half log sub 12 open paren x cubed minus 2 close paren minus 5 log sub 12 open paren x plus 1 close paren
B
4 log sub 12 x plus 1 half log sub 12 the fraction with numerator x cubed and denominator 2 minus 5 log sub 12 x plus the log base 12 of 1
C
4 log sub 12 x plus 1 half log sub 12 open paren x cubed minus 2 close paren minus 5 log sub 12 open paren x times 1 close paren
D
the log base the log base 12 of 4 of x plus 1 half log sub 12 open paren x cubed minus 2 close paren minus 5 log sub 12 x plus 1
13

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

A
0 point 5 5 7
B
0 point 6 2 0
C
0 point 2 3 3
D
1 point 7 9 6
14

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

A
16 thirds
B
5
C
4
D
1 third
15

Which graph represents an exponential decay function?

A
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.
B
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).
C
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).
D
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.
16

Which is an equivalent form of the expression 1800 times 1 point 2 raised to the negative t power ?

A
1800 times open paren 2 over 1 close paren to the t th power
B
1800 times 6 fifths to the t th power
C
1800 times 1 half to the t th power
D
1800 times 5 sixths to the t th power
17

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

A
y is equal to 2 times open paren 5 to the x th power close paren
B
y is equal to 5 to the x th power plus 2
C
y is equal to 2 to the x th power
D
y is equal to 5 raised to the x plus 2 power
18

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

A
negative 9
B
negative 3
C
3
D
9
19

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

A
x is equal to 3
B
x is equal to 9
C
x is equal to 3 halves
D
x is equal to 1 over 12
20

The formula for determining the frequency, f , of a note on a piano is f is equal to 440 times 2 raised to the h over 12 power , where h is the number of half-steps from the cap A above middle ​C on the keyboard. A note is six half-steps away from the cap A above middle ​C The frequency of the cap A above middle ​C is 440 Hz. How much greater is the frequency of the new note compared with the frequency of the cap A above middle ​C ?

A
29 point 3 percent
B
182 point 3 percent
C
70 point 7 percent
D
41 point 4 percent

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Mathematical Modeling: Part Two — Test Answers…