Question 1

Evaluate the expression using the graphs of y = f(x) and y = g(x).
-Evaluate (fg)(-1).

Accepted Answer

A)  0 
B)  -2 
C)  3 
D)  -1 
A)  0 
B)  -2 
C)  3 
D)  -1

Question 2

Change the exponential expression to an equivalent expression involving a logarithm.
-$$32 ^ { 2 / 5 } = 4$$

Accepted Answer

A)  $\log _ { 4 } 32 = \frac { 2 } { 5 }$ 
B)  $\log _ { 32 } 4 = \frac { 2 } { 5 }$ 
C)  $\log _ { 2 } 32 = \frac { 2 } { 5 }$ 
D)  $\frac { \log _ { 5 } 4 } { \log _ { 2 } 32 } = 32$ 
A)  $\log _ { 4 } 32 = \frac { 2 } { 5 }$ 
B)  $\log _ { 32 } 4 = \frac { 2 } { 5 }$ 
C)  $\log _ { 2 } 32 = \frac { 2 } { 5 }$ 
D)  $\frac { \log _ { 5 } 4 } { \log _ { 2 } 32 } = 32$

Question 3

Solve the problem.
-Find out how long it takes a $2,700 investment to double if it is invested at 7% compounded semiannually. Round to the nearest tenth of a year. Use the formula $\mathrm { A } = \mathrm { P } \left( 1 + \frac { \mathrm { r } } { \mathrm { n } } \right) ^ { \mathrm { nt } }$

Accepted Answer

A)  9.9 years 
B)  10.3 years 
C)  10.5 years 
D)  10.1 years 
A)  9.9 years 
B)  10.3 years 
C)  10.5 years 
D)  10.1 years

Question 4

Solve the problem.
-The logistic growth model $\mathrm { P } ( \mathrm { t } ) = \frac { 1 } { 1 + 6.69 \mathrm { e } ^ { - 0.753 \mathrm { t } } }$ represents the proportion of the total market of a new product as it penetrates the market t years after introduction. When will the product have 65% of the market?

Accepted Answer

A)  2.95 years 
B)  3.35 years 
C)  4.35 years 
D)  1.95 years 
A)  2.95 years 
B)  3.35 years 
C)  4.35 years 
D)  1.95 years

Question 5

Find the exact value of the logarithmic expression.
-$\log _ { 8 } 1$

Accepted Answer

A)  $\frac { 1 } { 8 }$ 
B)  0 
C)  1 
D)  8 
A)  $\frac { 1 } { 8 }$ 
B)  0 
C)  1 
D)  8

Question 6

Solve the problem.
-Money magazine reports that the percentage of trading days in which the Dasdaq loses or gains 2% or more has been increasing since 1995 indicating more volatility in the Dasdaq. Use a graphing utility to fit an exponential
Function to the data. Predict the percentage of trading days in 2001 having such swings in value. $\begin{array}{l|l}
\text { Year } & \% \text { of trading days } \
\hline 1995,0 & 2 \
1996,1 & 5 \
1997,2 & 8 \
1998,3 & 18 \
1999,4 & 23 \
2000,5 & 49
\end{array}$

Accepted Answer

A)  $y=2.353 e^{0.610 x}, 91 \text { days }$ 
B)  $\mathrm { y } = 1.669 \mathrm { x } 1.706,46$ days 
C)  $\mathrm { y } = 1.278 \mathrm { e } ^ { 0.611 \mathrm { x } } , 92 \text { days }$ 
D)  $\mathrm { y } = 1.849 \mathrm { e } ^ { 0.531 \mathrm { x } } , 76$ days 
A)  $y=2.353 e^{0.610 x}, 91 \text { days }$ 
B)  $\mathrm { y } = 1.669 \mathrm { x } 1.706,46$ days 
C)  $\mathrm { y } = 1.278 \mathrm { e } ^ { 0.611 \mathrm { x } } , 92 \text { days }$ 
D)  $\mathrm { y } = 1.849 \mathrm { e } ^ { 0.531 \mathrm { x } } , 76$ days

Question 7

Solve the equation.
-$\log _ { 6 } \left( x ^ { 2 } - 5 x \right) = 1$

Accepted Answer

A)  $\{ - 6,1 \}$ 
B)  $\{ 6 \}$ 
C)  $\{ 6 , - 1 \}$ 
D)  $\{ 1 \}$ 
A)  $\{ - 6,1 \}$ 
B)  $\{ 6 \}$ 
C)  $\{ 6 , - 1 \}$ 
D)  $\{ 1 \}$

Question 8

Solve the problem.
-The $\mathrm { pH }$ of a chemical solution is given by the formula
$$\mathrm { pH } = - \log _ { 10 } \left[ \mathrm { H } ^ { + } \right]$$
where $\left[ \mathrm { H } ^ { + } \right]$is the concentration of hydrogen ions in moles per liter.
Find the $\mathrm { pH }$ if the $\left[ \mathrm { H } ^ { + } \right] = 8.4 \times 10 ^ { - 1 }$.

Accepted Answer

A)  $0.08$ 
B)  $1.92$ 
C)  $0.92$ 
D)  $1.08$ 
A)  $0.08$ 
B)  $1.92$ 
C)  $0.92$ 
D)  $1.08$

Question 9

For the given functions f and g, find the requested composite function.
-$f ( x ) = \frac { 5 } { x - 1 } , \quad g ( x ) = \frac { 1 } { 6 x } ; \quad$ Find $( f \circ g ) ( x )$

Accepted Answer

A)  $\frac { 5 x } { 1 - 6 x }$ 
B)  $\frac { 1 \mathrm { x } - 1 } { 30 \mathrm { x } }$ 
C)  $\frac { 30 x } { 1 + 6 x }$ 
D)  $\frac { 30 x } { 1 - 6 x }$ 
A)  $\frac { 5 x } { 1 - 6 x }$ 
B)  $\frac { 1 \mathrm { x } - 1 } { 30 \mathrm { x } }$ 
C)  $\frac { 30 x } { 1 + 6 x }$ 
D)  $\frac { 30 x } { 1 - 6 x }$

Question 10

Approximate the value using a calculator. Express answer rounded to three decimal places.
-$3 ^ { 3.3 }$

Accepted Answer

A)  27.000 
B)  37.541 
C)  35.937 
D)  9.900 
A)  27.000 
B)  37.541 
C)  35.937 
D)  9.900

Question 11

Solve the equation.
-$\log _ { 3 } ( x + 1 ) = - 2$

Accepted Answer

A)  $\left\{ \frac { 10 } { 9 } \right\}$ 
B)  $\left\{ - \frac { 8 } { 9 } \right\}$ 
C)  $\{ - 1 \}$ 
D)  $\left\{ \frac { 5 } { 4 } \right\}$ 
A)  $\left\{ \frac { 10 } { 9 } \right\}$ 
B)  $\left\{ - \frac { 8 } { 9 } \right\}$ 
C)  $\{ - 1 \}$ 
D)  $\left\{ \frac { 5 } { 4 } \right\}$

Question 12

The graph of a logarithmic function is shown. Select the function which matches the graph.
-  A) $f ( x ) = \log _ { 2 } ( x - 2 )$

Accepted Answer

B)  $f ( x ) = \log _ { 2 } ( x + 2 )$ 
C)  $f ( x ) = \log _ { 2 } x - 2$ 
D)  $f ( x ) = \log _ { 2 } x$ 
B)  $f ( x ) = \log _ { 2 } ( x + 2 )$ 
C)  $f ( x ) = \log _ { 2 } x - 2$ 
D)  $f ( x ) = \log _ { 2 } x$

Question 13

Solve the equation.
-$$23 ^ { x } = 1$$

Accepted Answer

A)  $\{ 0 \}$ 
B)  $\left\{ \frac { 1 } { 23 } \right\}$ 
C)  $\{ 1 \}$ 
D)  $\varnothing$ 
A)  $\{ 0 \}$ 
B)  $\left\{ \frac { 1 } { 23 } \right\}$ 
C)  $\{ 1 \}$ 
D)  $\varnothing$

Question 14

Find the amount that results from the investment.
-$480 invested at 16% compounded quarterly after a period of 9 years

Accepted Answer

A)  $1,894.12 
B)  $1,825.42 
C)  $1,969.89 
D)  $1,489.89 
A)  $1,894.12 
B)  $1,825.42 
C)  $1,969.89 
D)  $1,489.89

Question 15

Approximate the value using a calculator. Express answer rounded to three decimal places.
-$\mathrm { e } ^ { 3.28 }$

Accepted Answer

A)  15.154 
B)  8.916 
C)  25.252 
D)  26.576 
A)  15.154 
B)  8.916 
C)  25.252 
D)  26.576

Question 16

Change the logarithmic expression to an equivalent expression involving an exponent.
-$$y = \log _ { 61 } x$$

Accepted Answer

The answer of Change the logarithmic expression to an equivalent...

Question 17

For the given functions f and g, find the requested composite function.
-$f ( x ) = \sqrt { x + 2 } , \quad g ( x ) = 8 x - 6 ; \quad$ Find $( f \circ g ) ( x )$

Accepted Answer

A)  $8 \sqrt { x - 4 }$ 
B)  $2 \sqrt { 2 x - 1 }$ 
C)  $8 \sqrt { x + 2 } - 6$ 
D)  $2 \sqrt { 2 x + 1 }$ 
A)  $8 \sqrt { x - 4 }$ 
B)  $2 \sqrt { 2 x - 1 }$ 
C)  $8 \sqrt { x + 2 } - 6$ 
D)  $2 \sqrt { 2 x + 1 }$

Question 18

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator.
-$\log _ { 4 } 24 - \log _ { 4 } 6$

Accepted Answer

A)  24 
B)  4 
C)  1 
D)  6 
A)  24 
B)  4 
C)  1 
D)  6

Question 19

Solve the equation.
-$$\log _ { 3 } x = 4$$

Accepted Answer

A)  {64} 
B)  {12} 
C)  {1.26} 
D)  {81} 
A)  {64} 
B)  {12} 
C)  {1.26} 
D)  {81}

Question 20

Decide whether or not the functions are inverses of each other.
-$$f ( x ) = ( x - 6 ) ^ { 2 } , x \geq 6 ; g ( x ) = \sqrt { x + 6 }$$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Evaluate the expression using the graphs of y = f(x) and y = g(x). -Evaluate (fg)(-1).

Change the exponential expression to an equivalent expression involving a logarithm. - $32 ^ { 2 / 5 } = 4$

Solve the problem. -Find out how long it takes a $2,700 investment to double if it is invested at 7% compounded semiannually. Round to the nearest tenth of a year. Use the formula $\mathrm { A } = \mathrm { P } \left( 1 + \frac { \mathrm { r } } { \mathrm { n } } \right) ^ { \mathrm { nt } }$

Find the exact value of the logarithmic expression. - $\log _ { 8 } 1$

Solve the equation. - $\log _ { 6 } \left( x ^ { 2 } - 5 x \right) = 1$

For the given functions f and g, find the requested composite function. - $f ( x ) = \frac { 5 } { x - 1 } , \quad g ( x ) = \frac { 1 } { 6 x } ; \quad$ Find $( f \circ g ) ( x )$

Approximate the value using a calculator. Express answer rounded to three decimal places. - $3 ^ { 3.3 }$

Solve the equation. - $\log _ { 3 } ( x + 1 ) = - 2$

Solve the equation. - $23 ^ { x } = 1$

Find the amount that results from the investment. -$480 invested at 16% compounded quarterly after a period of 9 years

Approximate the value using a calculator. Express answer rounded to three decimal places. - $\mathrm { e } ^ { 3.28 }$

Change the logarithmic expression to an equivalent expression involving an exponent. - $y = \log _ { 61 } x$

For the given functions f and g, find the requested composite function. - $f ( x ) = \sqrt { x + 2 } , \quad g ( x ) = 8 x - 6 ; \quad$ Find $( f \circ g ) ( x )$

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - $\log _ { 4 } 24 - \log _ { 4 } 6$

Solve the equation. - $\log _ { 3 } x = 4$

Decide whether or not the functions are inverses of each other. - $f ( x ) = ( x - 6 ) ^ { 2 } , x \geq 6 ; g ( x ) = \sqrt { x + 6 }$

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

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Exam 4: Exponential and Logarithmic Functions

Evaluate the expression using the graphs of y = f(x) and y = g(x). -Evaluate (fg)(-1).

Change the exponential expression to an equivalent expression involving a logarithm. - 322/5=432 ^ { 2 / 5 } = 4322/5=4

Find the exact value of the logarithmic expression. - log⁡81\log _ { 8 } 1log8​1

Solve the equation. - log⁡6(x2−5x)=1\log _ { 6 } \left( x ^ { 2 } - 5 x \right) = 1log6​(x2−5x)=1

For the given functions f and g, find the requested composite function. - f(x)=5x−1,g(x)=16x;f ( x ) = \frac { 5 } { x - 1 } , \quad g ( x ) = \frac { 1 } { 6 x } ; \quadf(x)=x−15​,g(x)=6x1​; Find (f∘g)(x)( f \circ g ) ( x )(f∘g)(x)

Approximate the value using a calculator. Express answer rounded to three decimal places. - 33.33 ^ { 3.3 }33.3

Solve the equation. - log⁡3(x+1)=−2\log _ { 3 } ( x + 1 ) = - 2log3​(x+1)=−2

Solve the equation. - 23x=123 ^ { x } = 123x=1