Question 1

Solve the equation.
-$$3 ^ { 1 + 2 x } = 27$$

Accepted Answer

A)  $\{ 9 \}$ 
B)  $\{ - 1 \}$ 
C)  $\{ 1 \}$ 
D)  $\{ 3 \}$ 
A)  $\{ 9 \}$ 
B)  $\{ - 1 \}$ 
C)  $\{ 1 \}$ 
D)  $\{ 3 \}$

Question 2

Find the inverse of the function and state its domain and range .
-$$\{ ( 9 , - 8 ) , ( 7 , - 7 ) , ( 5 , - 6 ) , ( 3 , - 5 ) \}$$

Accepted Answer

A)  $\{ ( - 7 , - 8 ) , ( - 8,5 ) , ( 9,7 ) , ( - 7 , - 6 ) \} ; \mathrm { D } = \{ ( - 7 , - 8,9 \} ; \mathrm { R } = \{ ( - 8,57 , - 6 \}$ 
B)  $\{ ( - 8,9 ) , ( - 7,7 ) , ( - 6,5 ) , ( - 5,3 ) \} ; \mathrm { D } = \{ - 8 , - 7 , - 6 , - 5 \} ; \mathrm { R } = \{ 9,7,5,3 \}$ 
C)  $\{ ( - 7 , - 8 ) , ( - 5,5 ) , ( 9,5 ) , ( - 7 , - 6 ) \} ; \mathrm { D } = \{ - 7 , - 5,9 \} ; \mathrm { R } = \{ - 8,5 , - 6 \}$ 
D)  $\left\{ \left( 9 , - \frac { 1 } { 8 } \right) , \left( 7 , - \frac { 1 } { 7 } \right) , \left( 5 , - \frac { 1 } { 6 } \right) , \left( 3 , - \frac { 1 } { 5 } \right) \right\} ; \mathrm { D } = \{ 9,7,5,3 \} , \mathrm { R } = \left\{ - \frac { 1 } { 8 } , - \frac { 1 } { 7 } , - \frac { 1 } { 6 } , - \frac { 1 } { 5 } \right\}$ 
A)  $\{ ( - 7 , - 8 ) , ( - 8,5 ) , ( 9,7 ) , ( - 7 , - 6 ) \} ; \mathrm { D } = \{ ( - 7 , - 8,9 \} ; \mathrm { R } = \{ ( - 8,57 , - 6 \}$ 
B)  $\{ ( - 8,9 ) , ( - 7,7 ) , ( - 6,5 ) , ( - 5,3 ) \} ; \mathrm { D } = \{ - 8 , - 7 , - 6 , - 5 \} ; \mathrm { R } = \{ 9,7,5,3 \}$ 
C)  $\{ ( - 7 , - 8 ) , ( - 5,5 ) , ( 9,5 ) , ( - 7 , - 6 ) \} ; \mathrm { D } = \{ - 7 , - 5,9 \} ; \mathrm { R } = \{ - 8,5 , - 6 \}$ 
D)  $\left\{ \left( 9 , - \frac { 1 } { 8 } \right) , \left( 7 , - \frac { 1 } { 7 } \right) , \left( 5 , - \frac { 1 } { 6 } \right) , \left( 3 , - \frac { 1 } { 5 } \right) \right\} ; \mathrm { D } = \{ 9,7,5,3 \} , \mathrm { R } = \left\{ - \frac { 1 } { 8 } , - \frac { 1 } { 7 } , - \frac { 1 } { 6 } , - \frac { 1 } { 5 } \right\}$

Question 3

Solve the problem.
-The half-life of carbon-14 is 5700 years. Find the age of a sample in which 8% of the radioactive nuclei
originally present have decayed.

Accepted Answer

The answer of Solve the problem.
-The half-life of carbon-14 is...

Question 4

The graph of an exponential function is given. Match the graph to one of the following functions.
-  A) $f ( x ) = 2 ^ { - x }$

Accepted Answer

B)  $f ( x ) = - 2 ^ { - x }$ 
C)  $f ( x ) = 2 ^ { x }$ 
D)  $f ( x ) = - 2 ^ { x }$ 
B)  $f ( x ) = - 2 ^ { - x }$ 
C)  $f ( x ) = 2 ^ { x }$ 
D)  $f ( x ) = - 2 ^ { x }$

Question 5

Solve the problem.
-A mechanic is testing the cooling system of a boat engine. He measures the engine's temperature over time. Use a graphing utility to fit a logistic function to the data. What is the carrying capacity of the cooling system? $\begin{array}{l|lllll}
\text { time, min } & 5 & 10 & 15 & 20 & 25 \
\hline \text { temperature, }^{\circ} \mathrm{F} & 100 & 180 & 270 & 300 & 305
\end{array}$

Accepted Answer

A)  $y = \frac { 306.53 } { 1 + 7.92 \mathrm { e } ^ { - 0.254 x } } , 307 ^ { \circ } \mathrm { F }$ 
B)  $y = \frac { 311.63 } { 1 + 8.1 \mathrm { e } ^ { - 0.253 \mathrm { x } } } , 312 ^ { \circ } \mathrm { F }$ 
C)  $y = \frac { 314.79 } { 1 + 7.86 \mathrm { e } ^ { - 1.22 \mathrm { x } } } , 315 ^ { \circ } \mathrm { F }$ 
D)  $y = \frac { 314.79 } { 1 + 7.86 \mathrm { e } ^ { - 0.246 \mathrm { x } } } , 315 ^ { \circ } \mathrm { F }$ 
A)  $y = \frac { 306.53 } { 1 + 7.92 \mathrm { e } ^ { - 0.254 x } } , 307 ^ { \circ } \mathrm { F }$ 
B)  $y = \frac { 311.63 } { 1 + 8.1 \mathrm { e } ^ { - 0.253 \mathrm { x } } } , 312 ^ { \circ } \mathrm { F }$ 
C)  $y = \frac { 314.79 } { 1 + 7.86 \mathrm { e } ^ { - 1.22 \mathrm { x } } } , 315 ^ { \circ } \mathrm { F }$ 
D)  $y = \frac { 314.79 } { 1 + 7.86 \mathrm { e } ^ { - 0.246 \mathrm { x } } } , 315 ^ { \circ } \mathrm { F }$

Question 6

Express y as a function of x. The constant C is a positive number.
-$\ln y = \ln 4 x + \ln C$

Accepted Answer

A)  $y = x + 4 C$ 
B)  $y = ( 4 x ) ^ { C }$ 
C)  $y = 4 x + C$ 
D)  $y = 4 C x$ 
A)  $y = x + 4 C$ 
B)  $y = ( 4 x ) ^ { C }$ 
C)  $y = 4 x + C$ 
D)  $y = 4 C x$

Question 7

Solve the equation.
-$$4 ^ { x } = 64$$

Accepted Answer

A)  $\{ 3 \}$ 
B)  $\{ 4 \}$ 
C)  $\{ 16 \}$ 
D)  $\{ 2 \}$ 
A)  $\{ 3 \}$ 
B)  $\{ 4 \}$ 
C)  $\{ 16 \}$ 
D)  $\{ 2 \}$

Question 8

Solve the equation.
-$$\log _ { 5 } 25 = x$$

Accepted Answer

A)  {5} 
B)  {2} 
C)  {30} 
D)  {125} 
A)  {5} 
B)  {2} 
C)  {30} 
D)  {125}

Question 9

Solve the problem.
-Between 8:30 a.m. and 9:30 a.m., cars drive through the Cappuccino Express at a rate of 12 cars per hour (0.2 per
minute). The following formula from probability can be used to determine the probability that a car will arrive within t
minutes of 8:30a.m. $F ( t ) = 1 - e ^ { - 0.2 t }$ Determine how many minutes are needed for the probability to reach 0.6.

Accepted Answer

The answer of Solve the problem.
-Between 8:30 a.m. and 9:30...

Question 10

For the given functions f and g, find the requested composite function.
-$f ( x ) = x ^ { 2 } - 5 , \quad g ( x ) = x ^ { 2 } - 8 ; \quad$ Find $( f \circ g ) ( x )$

Accepted Answer

A)  $x ^ { 4 } - 16 x ^ { 2 } + 59$ 
B)  $x ^ { 4 } + 17$ 
C)  $x ^ { 4 } + 59$ 
D)  $x ^ { 4 } - 10 x ^ { 2 } + 17$ 
A)  $x ^ { 4 } - 16 x ^ { 2 } + 59$ 
B)  $x ^ { 4 } + 17$ 
C)  $x ^ { 4 } + 59$ 
D)  $x ^ { 4 } - 10 x ^ { 2 } + 17$

Question 11

Find functions f and g so that f $f \circ g = H$
-$$H ( x ) = \frac { 1 } { x ^ { 2 } - 6 }$$

Accepted Answer

A)  $f ( x ) = \frac { 1 } { x } ; g ( x ) = \frac { 1 } { x ^ { 2 } } - 9$ 
B)  $f ( x ) = \frac { 1 } { x ^ { 2 } } - 9 ; g ( x ) = \frac { 1 } { x }$ 
C)  $f ( x ) = x ^ { 2 } - 6 ; g ( x ) = \frac { 1 } { x }$ 
D)  $f ( x ) = \frac { 1 } { x } , g ( x ) = x ^ { 2 } - 6$ 
A)  $f ( x ) = \frac { 1 } { x } ; g ( x ) = \frac { 1 } { x ^ { 2 } } - 9$ 
B)  $f ( x ) = \frac { 1 } { x ^ { 2 } } - 9 ; g ( x ) = \frac { 1 } { x }$ 
C)  $f ( x ) = x ^ { 2 } - 6 ; g ( x ) = \frac { 1 } { x }$ 
D)  $f ( x ) = \frac { 1 } { x } , g ( x ) = x ^ { 2 } - 6$

Question 12

The graph of an exponential function is given. Match the graph to one of the following functions.
-  A) $f ( x ) = 2 ^ { - x }$

Accepted Answer

B)  $f ( x ) = 2 ^ { x }$ 
C)  $f ( x ) = - 2 ^ { - x }$ 
D)  $f ( x ) = - 2 ^ { x }$ 
B)  $f ( x ) = 2 ^ { x }$ 
C)  $f ( x ) = - 2 ^ { - x }$ 
D)  $f ( x ) = - 2 ^ { x }$

Question 13

Decide whether the composite functions, f $$f \circ g$$ nd $\mathbf { g } \circ \mathrm { f }$ f, are equal to x.
-$f ( x ) = x ^ { 2 } + 1 , g ( x ) = \sqrt { x } - 1$

Accepted Answer

A)  No, yes 
B)  No, no 
C)  Yes, yes 
D)  Yes, no 
A)  No, yes 
B)  No, no 
C)  Yes, yes 
D)  Yes, no

Question 14

Indicate whether the function is one-to-one.
-{(7, -3), (3, -7), (-2, 9), (2, -9)}

Accepted Answer

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

Question 15

Solve the problem.
-Julio figures that he can save $5000 per year. If, at the end of each year, he invests the money in a certificate of
deposit (CD) which pays 7% interest annually, how much money will he have saved in six years?

Accepted Answer

The answer of Solve the problem.
-Julio figures that he can...

Question 16

Solve the exponential equation. Express the solution set in terms of natural logarithms.
-$$4 ^ { x + 4 } = 5 ^ { 2 x + 5 }$$

Accepted Answer

A)  $\{ 7 \ln 5 - 5 \ln 4 \}$ 
B)  $\{ \ln 5 - \ln 4 \}$ 
C)  $\left\{ \frac { 5 \ln 5 - 4 \ln 4 } { \ln 4 - 2 \ln 5 } \right\}$ 
D)  $\left\{ \ln \left[ \frac { 5 ^ { 5 } } { 4 ^ { 4 } } - \frac { 4 } { 5 ^ { 2 } } \right] \right\}$ 
A)  $\{ 7 \ln 5 - 5 \ln 4 \}$ 
B)  $\{ \ln 5 - \ln 4 \}$ 
C)  $\left\{ \frac { 5 \ln 5 - 4 \ln 4 } { \ln 4 - 2 \ln 5 } \right\}$ 
D)  $\left\{ \ln \left[ \frac { 5 ^ { 5 } } { 4 ^ { 4 } } - \frac { 4 } { 5 ^ { 2 } } \right] \right\}$

Question 17

Solve the problem.
-The number of men dying of AIDS (in thousands) since 1987 is modeled by $$y = 17.3 + 10.06 ( \ln x )$$ where x represents the number of years after 1987. Use this model to predict the number of AIDS deaths among men in
1994. Express answer rounded to the nearest hundred men.

Accepted Answer

A)  36,900 
B)  26,000 
C)  37,000 
D)  25,800 
A)  36,900 
B)  26,000 
C)  37,000 
D)  25,800

Question 18

Solve the equation.
-$\log _ { 20 } \left( x ^ { 2 } - x \right) = 1$

Accepted Answer

A)  $\{ - 4,5 \}$ 
B)  $\{ 4,5 \}$ 
C)  $\{ - 4 , - 5 \}$ 
D)  $\{ 1,20 \}$ 
A)  $\{ - 4,5 \}$ 
B)  $\{ 4,5 \}$ 
C)  $\{ - 4 , - 5 \}$ 
D)  $\{ 1,20 \}$

Question 19

For the given functions f and g, find the requested composite function value.
-$$f ( x ) = 2 x + 2 , \quad g ( x ) = 2 x ^ { 2 } + 3 ; \quad \text { Find } ( f \circ f ) ( 0 )$$

Accepted Answer

A)  21 
B)  8 
C)  6 
D)  11 
A)  21 
B)  8 
C)  6 
D)  11

Question 20

Solve the problem.
-The formula P $P = 14.7 e ^ { - 0.21 x }$ gives the average atmospheric pressure, P, in pounds per square inch, at an altitude x, in miles above sea level. Find the average atmospheric pressure for an altitude of 2.3 miles. Round
Your answer to the nearest tenth. A) $7.8 \mathrm { lb } / \mathrm { in } ^ { 2 }$

Accepted Answer

B)  $9.1 \mathrm { lb } / \mathrm { in } ^ { 2 }$ 
C)  $8.4 \mathrm { lb } / \mathrm { in } ^ { 2 }$ 
D)  $11.0 \mathrm { lb } /$ in. $^ { 2 }$ 
B)  $9.1 \mathrm { lb } / \mathrm { in } ^ { 2 }$ 
C)  $8.4 \mathrm { lb } / \mathrm { in } ^ { 2 }$ 
D)  $11.0 \mathrm { lb } /$ in. $^ { 2 }$

Solve the equation. - $3 ^ { 1 + 2 x } = 27$

Find the inverse of the function and state its domain and range . - $\{ ( 9 , - 8 ) , ( 7 , - 7 ) , ( 5 , - 6 ) , ( 3 , - 5 ) \}$

Solve the problem. -The half-life of carbon-14 is 5700 years. Find the age of a sample in which 8% of the radioactive nuclei originally present have decayed.

Solve the problem. -A mechanic is testing the cooling system of a boat engine. He measures the engine's temperature over time. Use a graphing utility to fit a logistic function to the data. What is the carrying capacity of the cooling system? time, min 5 10 15 20 25 100 180 270 300 305

Express y as a function of x. The constant C is a positive number. - $\ln y = \ln 4 x + \ln C$

Solve the equation. - $4 ^ { x } = 64$

Solve the equation. - $\log _ { 5 } 25 = x$

For the given functions f and g, find the requested composite function. - $f ( x ) = x ^ { 2 } - 5 , \quad g ( x ) = x ^ { 2 } - 8 ; \quad$ Find $( f \circ g ) ( x )$

Find functions f and g so that f $f \circ g = H$ - $H ( x ) = \frac { 1 } { x ^ { 2 } - 6 }$

Decide whether the composite functions, f $f \circ g$ nd $\mathbf { g } \circ \mathrm { f }$ f, are equal to x. - $f ( x ) = x ^ { 2 } + 1 , g ( x ) = \sqrt { x } - 1$

Indicate whether the function is one-to-one. -{(7, -3), (3, -7), (-2, 9), (2, -9)}

Solve the problem. -Julio figures that he can save $5000 per year. If, at the end of each year, he invests the money in a certificate of deposit (CD) which pays 7% interest annually, how much money will he have saved in six years?

Solve the exponential equation. Express the solution set in terms of natural logarithms. - $4 ^ { x + 4 } = 5 ^ { 2 x + 5 }$

Solve the problem. -The number of men dying of AIDS (in thousands) since 1987 is modeled by $y = 17.3 + 10.06 ( \ln x )$ where x represents the number of years after 1987. Use this model to predict the number of AIDS deaths among men in 1994. Express answer rounded to the nearest hundred men.

Solve the equation. - $\log _ { 20 } \left( x ^ { 2 } - x \right) = 1$

For the given functions f and g, find the requested composite function value. - $f ( x ) = 2 x + 2 , \quad g ( x ) = 2 x ^ { 2 } + 3 ; \quad \text { Find } ( f \circ f ) ( 0 )$

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

Review

Filters

Exam 4: Exponential and Logarithmic Functions

Solve the equation. - 31+2x=273 ^ { 1 + 2 x } = 2731+2x=27

Find the inverse of the function and state its domain and range . - {(9,−8),(7,−7),(5,−6),(3,−5)}\{ ( 9 , - 8 ) , ( 7 , - 7 ) , ( 5 , - 6 ) , ( 3 , - 5 ) \}{(9,−8),(7,−7),(5,−6),(3,−5)}