Question 1

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator.
-$4 ^ { \log _ { 4 } 0.473 }$

Accepted Answer

A)  477 
B)  4 
C)  $2.114$ 
D)  $0.473$ 
A)  477 
B)  4 
C)  $2.114$ 
D)  $0.473$

Question 2

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-Which of the two rates would yield the larger amount in 1 year: 5.2% compounded monthly or 5.1% compounded daily?

Accepted Answer

A)  5.2% compounded monthly 
B)  5.1% compounded daily 
C)  They will yield the same amount. 
A)  5.2% compounded monthly 
B)  5.1% compounded daily 
C)  They will yield the same amount.

Question 3

Graph the function.
-$f(x)=-4 \ln x$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 4

Determine whether the given function is exponential or not. If it is exponential, identify the value of the base a.
-$\begin{array}{rl}
\hline x & H(x) \
\hline-1 & 3 \
0 & 7 \
1 & 11 \
2 & 15 \
3 & 19
\end{array}$

Accepted Answer

A)  Exponential; $a = 3$ 
B)  Exponential; $a = 4$ 
C)  Exponential; $a = 7$ 
D)  Not exponential 
A)  Exponential; $a = 3$ 
B)  Exponential; $a = 4$ 
C)  Exponential; $a = 7$ 
D)  Not exponential

Question 5

Write the word or phrase that best completes each statement or answers the question.
-In 1992 , the population of a country was estimated at 5 million. For any subsequent year, the population, $\mathrm { P } ( \mathrm { t } )$ (in millions), can be modeled using the equation $\mathrm { P } ( \mathrm { t } ) = \frac { 250 } { 5 + 44.99 \mathrm { e } ^ { - 0.0208 \mathrm { t } } }$, where $t$ is the number of years since 1992. Determine the year when the population will be 39 million.

Accepted Answer

in about 166.47 year

Question 6

Choose the one alternative that best completes the statement or answers the question.
The graph of a logarithmic function is shown. Select the function which matches the graph.
-

Accepted Answer

A)  $y = \log ( x )$ 
B)  $y = \log ( - x )$ 
C)  $y = - \log ( - x )$ 
D)  $y = - \log ( x )$ 
A)  $y = \log ( x )$ 
B)  $y = \log ( - x )$ 
C)  $y = - \log ( - x )$ 
D)  $y = - \log ( x )$

Question 7

Graph the function.
-$$\mathrm { f } ( \mathrm { x } ) = \left( \frac { 1 } { 3 } \right) ^ { \mathrm { x } }$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 8

Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
-The weight $\mathrm { W }$ of a bird's brain (in ounces) is related to the volume $\mathrm { V }$ of the bird's skull (in cubic ounces) through the function $W ( V ) = 3.55 \sqrt [ 3 ] { V } + 1.23$.
(a) Express the skull volume $V$ as a function of brain weight $W$.
(b) Predict the skull volume of a bird whose brain weighs 3 oz.

Accepted Answer

The answer of Write the word or phrase that best...

Question 9

Choose the one alternative that best completes the statement or answers the question.
The graph of a logarithmic function is shown. Select the function which matches the graph.
-

Accepted Answer

A)  $f ( x ) = \log _ { 3 } ( x + 2 )$ 
B)  $f ( x ) = \log _ { 3 } x - 2$ 
C)  $f ( x ) = \log _ { 3 } ( x - 2 )$ 
D)  $f ( x ) = \log _ { 3 } x$ 
A)  $f ( x ) = \log _ { 3 } ( x + 2 )$ 
B)  $f ( x ) = \log _ { 3 } x - 2$ 
C)  $f ( x ) = \log _ { 3 } ( x - 2 )$ 
D)  $f ( x ) = \log _ { 3 } x$

Question 10

Write the word or phrase that best completes each statement or answers the question.
-The concentration of alcohol in a person's blood is measurable. Suppose that the risk R (given as a percent) of having an
accident while driving a car can be modeled by the equation $$\mathrm { R } = 5 \mathrm { e } ^ { \mathrm { kx } }$$ where x is the variable concentration of alcohol in the blood and k is a constant.
Suppose that a concentration of alcohol in the blood of 0.07 results in a 10% risk (R = 10) of an accident. Find the
constant k in the equation.
Using this value of k, what is the risk if the concentration is 0.11?

Accepted Answer

The answer of Write the word or phrase that best...

Question 11

Use the graph of the given one-to-one function to sketch the graph of the inverse function. For convenience, the graph of
y = x is also given.
-

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 12

Choose the one alternative that best completes the statement or answers the question.
-Conservationists tagged 130 black-nosed rabbits in a national forest in 1990. In 1,991, they tagged 260 black-nosed rabbits in the same range. If the rabbit population follows the exponential law, how many rabbits
Will be in the range 9 years from 1990?

Accepted Answer

A)  66,560 
B)  281 
C)  133,120 
D)  140 
A)  66,560 
B)  281 
C)  133,120 
D)  140

Question 13

Use transformations to graph the function.
-$$\text { Use the graph of } \log _ { 4 } x \text { to obtain the graph of } f ( x ) = \log _ { 4 } ( x - 1 ) \text {. }$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 14

Choose the one alternative that best completes the statement or answers the question.
-A thermometer reading $33 ^ { \circ } \mathrm { F }$ is brought into a room with a constant temperature of $80 ^ { \circ } \mathrm { F }$. If the thermometer reads $45 ^ { \circ } \mathrm { F }$ after 4 minutes, what will it read after being in the room for 6 minutes? Assume the cooling follows Newton's Law of Cooling:
$$\mathrm { U } = \mathrm { T } + \left( \mathrm { U } _ { \mathrm { O } } - \mathrm { T } \right) \mathrm { e } ^ { \mathrm { kt } } \text {. }$$
(Round your answer to two decimal places.)

Accepted Answer

A)  $25.32 ^ { \circ } \mathrm { F }$ 
B)  $71.98 ^ { \circ } \mathrm { F }$ 
C)  $49.8 ^ { \circ } \mathrm { F }$ 
D)  $110.2 ^ { \circ } \mathrm { F }$ 
A)  $25.32 ^ { \circ } \mathrm { F }$ 
B)  $71.98 ^ { \circ } \mathrm { F }$ 
C)  $49.8 ^ { \circ } \mathrm { F }$ 
D)  $110.2 ^ { \circ } \mathrm { F }$

Question 15

Solve the equation.
-$$\log _ { 4 } ( x + 2 ) = 2 + \log _ { 4 } ( x - 4 )$$

Accepted Answer

A)  $\left\{ - \frac { 22 } { 5 } \right\}$ 
B)  $\left\{ - \frac { 2 } { 5 } \right\}$ 
C)  $\left\{ \frac { 2 } { 5 } \right\}$ 
D)  $\left\{ \frac { 22 } { 5 } \right\}$ 
A)  $\left\{ - \frac { 22 } { 5 } \right\}$ 
B)  $\left\{ - \frac { 2 } { 5 } \right\}$ 
C)  $\left\{ \frac { 2 } { 5 } \right\}$ 
D)  $\left\{ \frac { 22 } { 5 } \right\}$

Question 16

Find the value of the expression.
-Let $\log _ { \mathrm { b } } \mathrm { A } = 3$ and $\log _ { \mathrm { b } } \mathrm { B } = - 4$. Find $\log _ { \mathrm { b } } \mathrm { AB }$.

Accepted Answer

A)  $- 1$ 
B)  12 
C)  7 
D)  $- 12$ 
A)  $- 1$ 
B)  12 
C)  7 
D)  $- 12$

Question 17

Solve the equation.
-$e ^ { 6 x - 1 } = \left( e ^ { 4 } \right) ^ { - x }$

Accepted Answer

A)  $\{ 0 \}$ 
B)  $\left\{ \frac { 5 } { 7 } \right\}$ 
C)  $\left\{ \frac { 1 } { 10 } \right\}$ 
D)  $\left\{ \frac { 1 } { 2 } \right\}$ 
A)  $\{ 0 \}$ 
B)  $\left\{ \frac { 5 } { 7 } \right\}$ 
C)  $\left\{ \frac { 1 } { 10 } \right\}$ 
D)  $\left\{ \frac { 1 } { 2 } \right\}$

Question 18

The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve.
-$$f ( x ) = \frac { 4 } { x }$$

Accepted Answer

A)  Function is its own inverse
  
B) 
  
A)  Function is its own inverse
  
B)

Question 19

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 20

The graph of an exponential function is given. Match the graph to one of the following functions.
-

Accepted Answer

A)  $f ( x ) = 4 ^ { x }$ 
B)  $f ( x ) = 4 ^ { x } - 2$ 
C)  $f ( x ) = 4 ^ { x + 2 }$ 
D)  $f ( x ) = 4 ^ { x } + 2$ 
A)  $f ( x ) = 4 ^ { x }$ 
B)  $f ( x ) = 4 ^ { x } - 2$ 
C)  $f ( x ) = 4 ^ { x + 2 }$ 
D)  $f ( x ) = 4 ^ { x } + 2$

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - $4 ^ { \log _ { 4 } 0.473 }$

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Which of the two rates would yield the larger amount in 1 year: 5.2% compounded monthly or 5.1% compounded daily?

Graph the function. - $f(x)=-4 \ln x$ $Graph the function. - f(x)=-4 \ln x$

Determine whether the given function is exponential or not. If it is exponential, identify the value of the base a. - x H(x) -1 3 0 7 1 11 2 15 3 19

Choose the one alternative that best completes the statement or answers the question. The graph of a logarithmic function is shown. Select the function which matches the graph. -

Graph the function. - $\mathrm { f } ( \mathrm { x } ) = \left( \frac { 1 } { 3 } \right) ^ { \mathrm { x } }$ $Graph the function. - \mathrm { f } ( \mathrm { x } ) = \left( \frac { 1 } { 3 } \right) ^ { \mathrm { x } }$

Choose the one alternative that best completes the statement or answers the question. The graph of a logarithmic function is shown. Select the function which matches the graph. -

Use the graph of the given one-to-one function to sketch the graph of the inverse function. For convenience, the graph of y = x is also given. -

Solve the equation. - $\log _ { 4 } ( x + 2 ) = 2 + \log _ { 4 } ( x - 4 )$

Find the value of the expression. -Let $\log _ { \mathrm { b } } \mathrm { A } = 3$ and $\log _ { \mathrm { b } } \mathrm { B } = - 4$ . Find $\log _ { \mathrm { b } } \mathrm { AB }$ .

Solve the equation. - $e ^ { 6 x - 1 } = \left( e ^ { 4 } \right) ^ { - x }$

The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve. - $f ( x ) = \frac { 4 } { x }$ $The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve. - f ( x ) = \frac { 4 } { x }$

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

The graph of an exponential function is given. Match the graph to one of the following functions. -

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

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 4: Exponential and Logarithmic Functions

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - 4log⁡40.4734 ^ { \log _ { 4 } 0.473 }4log4​0.473

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Which of the two rates would yield the larger amount in 1 year: 5.2% compounded monthly or 5.1% compounded daily?

Graph the function. - f(x)=−4ln⁡xf(x)=-4 \ln xf(x)=−4lnx

Determine whether the given function is exponential or not. If it is exponential, identify the value of the base a. - x H(x) -1 3 0 7 1 11 2 15 3 19

Choose the one alternative that best completes the statement or answers the question. The graph of a logarithmic function is shown. Select the function which matches the graph. -

Graph the function. - f(x)=(13)x\mathrm { f } ( \mathrm { x } ) = \left( \frac { 1 } { 3 } \right) ^ { \mathrm { x } }f(x)=(31​)x

Choose the one alternative that best completes the statement or answers the question. The graph of a logarithmic function is shown. Select the function which matches the graph. -

Use the graph of the given one-to-one function to sketch the graph of the inverse function. For convenience, the graph of y = x is also given. -

Solve the equation. - log⁡4(x+2)=2+log⁡4(x−4)\log _ { 4 } ( x + 2 ) = 2 + \log _ { 4 } ( x - 4 )log4​(x+2)=2+log4​(x−4)

Find the value of the expression. -Let log⁡bA=3\log _ { \mathrm { b } } \mathrm { A } = 3logb​A=3 and log⁡bB=−4\log _ { \mathrm { b } } \mathrm { B } = - 4logb​B=−4 . Find log⁡bAB\log _ { \mathrm { b } } \mathrm { AB }logb​AB .

Solve the equation. - e6x−1=(e4)−xe ^ { 6 x - 1 } = \left( e ^ { 4 } \right) ^ { - x }e6x−1=(e4)−x

The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve. - f(x)=4xf ( x ) = \frac { 4 } { x }f(x)=x4​

Approximate the value using a calculator. Express answer rounded to three decimal places. - e3.28\mathrm { e } ^ { 3.28 }e3.28

The graph of an exponential function is given. Match the graph to one of the following functions. -

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

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - $4 ^ { \log _ { 4 } 0.473 }$

Graph the function. - $f(x)=-4 \ln x$ $Graph the function. - f(x)=-4 \ln x$

Graph the function. - $\mathrm { f } ( \mathrm { x } ) = \left( \frac { 1 } { 3 } \right) ^ { \mathrm { x } }$ $Graph the function. - \mathrm { f } ( \mathrm { x } ) = \left( \frac { 1 } { 3 } \right) ^ { \mathrm { x } }$

Solve the equation. - $\log _ { 4 } ( x + 2 ) = 2 + \log _ { 4 } ( x - 4 )$

Find the value of the expression. -Let $\log _ { \mathrm { b } } \mathrm { A } = 3$ and $\log _ { \mathrm { b } } \mathrm { B } = - 4$ . Find $\log _ { \mathrm { b } } \mathrm { AB }$ .

Solve the equation. - $e ^ { 6 x - 1 } = \left( e ^ { 4 } \right) ^ { - x }$

The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve. - $f ( x ) = \frac { 4 } { x }$ $The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve. - f ( x ) = \frac { 4 } { x }$

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