Question 1

without graphing, describe the shape of the graph of the function and complete the ordered pairs $(0,1)$ and $(1$,$) .$
-$f(x)=7^{0.4 x}$

Accepted Answer

A)  The graph lies above the $x$-axis, falls from left to right, with the negative $x$-axis as a horizontal asymptote; $(0,7)$ and $\left(1,7^{0.4}\right)$. 
B)  The graph lies below the $x$-axis, rises from left to right, with the negative $x$-axis as a horizontal asymptote; $(0,1)$ and $\left(1,7^{4}\right)$. 
C)  The graph lies above the $x$-axis, rises from left to right, with the negative $x$-axis as a horizontal asymptote; $(0,1)$ and $\left(1,7^{0.4}\right)$. 
D)  The graph lies below the $x$-axis, falls from right to left, with the negative $x$-axis as a horizontal asymptote; $(0,7)$ and $\left(1,7^{4}\right)$. 
A)  The graph lies above the $x$-axis, falls from left to right, with the negative $x$-axis as a horizontal asymptote; $(0,7)$ and $\left(1,7^{0.4}\right)$. 
B)  The graph lies below the $x$-axis, rises from left to right, with the negative $x$-axis as a horizontal asymptote; $(0,1)$ and $\left(1,7^{4}\right)$. 
C)  The graph lies above the $x$-axis, rises from left to right, with the negative $x$-axis as a horizontal asymptote; $(0,1)$ and $\left(1,7^{0.4}\right)$. 
D)  The graph lies below the $x$-axis, falls from right to left, with the negative $x$-axis as a horizontal asymptote; $(0,7)$ and $\left(1,7^{4}\right)$.

Question 2

Find the value of the expression.
-$\log _{4} \frac{1}{4}$

Accepted Answer

A)  1 
B)  -1 
C)  4 
D)  0 
A)  1 
B)  -1 
C)  4 
D)  0

Question 3

Classify the function as a linear, quadratic, or exponential.
-$f(x)=-x$

Accepted Answer

A)  Quadratic 
B)  Exponential 
C)  Linear 
A)  Quadratic 
B)  Exponential 
C)  Linear

Question 4

Solve the problem.
-Suppose the amount of a radioactive element remaining in a sample of 100 milligrams after $x$ years can be described by $\mathrm{A}(\mathrm{x})=100 \mathrm{e}^{-0.01679 \mathrm{x}}$. How much is remaining after 194 years? Round the answer to the nearest hundredth of a milligram.

Accepted Answer

A)  0.04 milligrams 
B)  2597.83 milligrams 
C)  325.73 milligrams 
D)  3.85 milligrams 
A)  0.04 milligrams 
B)  2597.83 milligrams 
C)  325.73 milligrams 
D)  3.85 milligrams

Question 5

Solve the problem.
-The population of a particular city is increasing at a rate proportional to its size. It follows the function $\mathrm{P}(\mathrm{t})=1+\mathrm{ke}^{0.08 \mathrm{t}}$ where $\mathrm{k}$ is a constant and $\mathrm{t}$ is the time in years. If the current population is 29,000 , in how many years is the population expected to be 72,500 ?

Accepted Answer

A)  79 year(s) 
B)  5 years(s) 
C)  6 year(s) 
D)  11 year(s) 
A)  79 year(s) 
B)  5 years(s) 
C)  6 year(s) 
D)  11 year(s)

Question 6

Solve the equation.
-$\log x^{2}=(\log x)^{2}$

Accepted Answer

A)  1,100 
B)  0,1 
C)  1, 2 
D)  $1,10.000$ 
A)  1,100 
B)  0,1 
C)  1, 2 
D)  $1,10.000$

Question 7

Solve the problem.
-Use a graphing calculator to predict about how many widgets will be produced in 2004.

Accepted Answer

A)  11 million 
B)  60 million 
C)  20 million 
D)  44 million 
A)  11 million 
B)  60 million 
C)  20 million 
D)  44 million

Question 8

Evaluate the expression.
-$\log _{41} 97.52$

Accepted Answer

A)  0.8108 
B)  2.3785 
C)  1.2333 
D)  1.9891 
A)  0.8108 
B)  2.3785 
C)  1.2333 
D)  1.9891

Question 9

Convert to exponential form.
-$\log _{4} 64=3$

Accepted Answer

A)  $64^{3}=4$ 
B)  $4^{64}=3$ 
C)  $4^{3}=64$ 
D)  $3^{4}=64$ 
A)  $64^{3}=4$ 
B)  $4^{64}=3$ 
C)  $4^{3}=64$ 
D)  $3^{4}=64$

Question 10

Write the logarithmic and exponential equations associated with the display.
-$f(x)=\log x$

Accepted Answer

A)  $\log 0.77815125038=6 ; 10^{6}=0.77815125038$ 
B)  $\log 6=1.79175946923 ; 10^{1.79175946923}=6$ 
C)  $\log 6=0.77815125038 ; 10^{0.77815125038}=6$ 
D)  $\log 1.79175946923=6 ; 10^{6}=1.79175946923$ 
A)  $\log 0.77815125038=6 ; 10^{6}=0.77815125038$ 
B)  $\log 6=1.79175946923 ; 10^{1.79175946923}=6$ 
C)  $\log 6=0.77815125038 ; 10^{0.77815125038}=6$ 
D)  $\log 1.79175946923=6 ; 10^{6}=1.79175946923$

Question 11

Solve the equation.
-$2 \mathrm{e}^{2 \mathrm{x}-5}=10$

Accepted Answer

A)  -1.695 
B)  7.500 
C)  3.076 
D)  3.305 
A)  -1.695 
B)  7.500 
C)  3.076 
D)  3.305

Question 12

Match the equation to the graph.
-

Accepted Answer

A)  $y=10^{x}$ 
B)  $y=e^{x}$ 
C)  $y=\log x$ 
D)  $y=\ln x$ 
A)  $y=10^{x}$ 
B)  $y=e^{x}$ 
C)  $y=\log x$ 
D)  $y=\ln x$

Question 13

Solve the problem.
-The decay of $289 \mathrm{mg}$ of an isotope is given by $A(t)=289 e^{-0.027 t}$, where $t$ is time in years. Find the amount left after 4 years.

Accepted Answer

A)  259 
B)  253 
C)  130 
D)  281 
A)  259 
B)  253 
C)  130 
D)  281

Question 14

Solve the equation for $s$.
-$\log (4+r)=\log (3 s-2)$

Accepted Answer

A)  $\log 3+r$ 
B)  $\frac{3}{6+r}$ 
C)  $\log (6+r)$ 
D)  $\frac{6+r}{3}$ 
A)  $\log 3+r$ 
B)  $\frac{3}{6+r}$ 
C)  $\log (6+r)$ 
D)  $\frac{6+r}{3}$

Question 15

Provide an appropriate response.
-Explain why log2 13 is between 3 and 4.

Accepted Answer

log₂ 8 = 3 and log₂ 16 = 4. Sinc

Question 16

Graph the function.
-$y=\log _{5}(x-1)$

Accepted Answer

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

Question 17

Provide an appropriate response.
-The graph of an exponential function is given. Which of the following is the correct equation of the function?

Accepted Answer

A)  $y=0.31^{x}$ 
B)  $y=2.4^{x}$ 
C)  $\mathrm{y}=1.8^{\mathrm{x}}$ 
D)  $y=0.45^{x}$ 
A)  $y=0.31^{x}$ 
B)  $y=2.4^{x}$ 
C)  $\mathrm{y}=1.8^{\mathrm{x}}$ 
D)  $y=0.45^{x}$

Question 18

Graph the function.
-$f(x)=3^{-x}$

Accepted Answer

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

Question 19

Graph the function.
-$f(x)=2(x-2)$

Accepted Answer

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

Question 20

Provide an appropriate response.
-Can you solve this equation without using logarithms? 5 = 3x Why or why not?

Accepted Answer

No, because 5 and 3

without graphing, describe the shape of the graph of the function and complete the ordered pairs $(0,1)$ and $(1$ , $) .$ - $f(x)=7^{0.4 x}$

Find the value of the expression. - $\log _{4} \frac{1}{4}$

Classify the function as a linear, quadratic, or exponential. - $f(x)=-x$

Solve the problem. -Suppose the amount of a radioactive element remaining in a sample of 100 milligrams after $x$ years can be described by $\mathrm{A}(\mathrm{x})=100 \mathrm{e}^{-0.01679 \mathrm{x}}$ . How much is remaining after 194 years? Round the answer to the nearest hundredth of a milligram.

Solve the equation. - $\log x^{2}=(\log x)^{2}$

Solve the problem. -Use a graphing calculator to predict about how many widgets will be produced in 2004.

Evaluate the expression. - $\log _{41} 97.52$

Convert to exponential form. - $\log _{4} 64=3$

Write the logarithmic and exponential equations associated with the display. - $f(x)=\log x$ $Write the logarithmic and exponential equations associated with the display. - f(x)=\log x$

Solve the equation. - $2 \mathrm{e}^{2 \mathrm{x}-5}=10$

Match the equation to the graph. -

Solve the problem. -The decay of $289 \mathrm{mg}$ of an isotope is given by $A(t)=289 e^{-0.027 t}$ , where $t$ is time in years. Find the amount left after 4 years.

Solve the equation for $s$ . - $\log (4+r)=\log (3 s-2)$

Provide an appropriate response. -Explain why log2 13 is between 3 and 4.

Graph the function. - $y=\log _{5}(x-1)$ $Graph the function. - y=\log _{5}(x-1)$

Provide an appropriate response. -The graph of an exponential function is given. Which of the following is the correct equation of the function?

Graph the function. - $f(x)=3^{-x}$ $Graph the function. - f(x)=3^{-x}$

Graph the function. - $f(x)=2(x-2)$

Provide an appropriate response. -Can you solve this equation without using logarithms? 5 = 3^x Why or why not?

Algebra and Equations

Graphs, Lines, and Inequalities

Functions and Graphs

Mathematics of Finance

Systems of Linear Equations and Matrices

Linear Programming

Sets and Probability

Counting, Probability Distributions, and Further Topics in Probability

Introduction to Statistics

Differential Calculus

Applications of the Derivative

Integral Calculus

Multivariate Calculus

Filters

Exam 4: Exponential and Logarithmic Functions

without graphing, describe the shape of the graph of the function and complete the ordered pairs (0,1)(0,1)(0,1) and (1(1(1 , ).) .). - f(x)=70.4xf(x)=7^{0.4 x}f(x)=70.4x

Find the value of the expression. - log⁡414\log _{4} \frac{1}{4}log4​41​

Classify the function as a linear, quadratic, or exponential. - f(x)=−xf(x)=-xf(x)=−x

Solve the equation. - log⁡x2=(log⁡x)2\log x^{2}=(\log x)^{2}logx2=(logx)2

Solve the problem. -Use a graphing calculator to predict about how many widgets will be produced in 2004.

Evaluate the expression. - log⁡4197.52\log _{41} 97.52log41​97.52

Convert to exponential form. - log⁡464=3\log _{4} 64=3log4​64=3

Write the logarithmic and exponential equations associated with the display. - f(x)=log⁡xf(x)=\log xf(x)=logx

Solve the equation. - 2e2x−5=102 \mathrm{e}^{2 \mathrm{x}-5}=102e2x−5=10

Match the equation to the graph. -

Solve the problem. -The decay of 289mg289 \mathrm{mg}289mg of an isotope is given by A(t)=289e−0.027tA(t)=289 e^{-0.027 t}A(t)=289e−0.027t , where ttt is time in years. Find the amount left after 4 years.

Solve the equation for sss . - log⁡(4+r)=log⁡(3s−2)\log (4+r)=\log (3 s-2)log(4+r)=log(3s−2)

Provide an appropriate response. -Explain why log2 13 is between 3 and 4.

Graph the function. - y=log⁡5(x−1)y=\log _{5}(x-1)y=log5​(x−1)

Provide an appropriate response. -The graph of an exponential function is given. Which of the following is the correct equation of the function?

Graph the function. - f(x)=3−xf(x)=3^{-x}f(x)=3−x

Graph the function. - f(x)=2(x−2)f(x)=2(x-2)f(x)=2(x−2)

Provide an appropriate response. -Can you solve this equation without using logarithms? 5 = 3x Why or why not?

Algebra and Equations

Graphs, Lines, and Inequalities

Functions and Graphs

Mathematics of Finance

Systems of Linear Equations and Matrices

Linear Programming

Sets and Probability

Counting, Probability Distributions, and Further Topics in Probability

Introduction to Statistics

Differential Calculus

Applications of the Derivative

Integral Calculus

Multivariate Calculus

Filters

without graphing, describe the shape of the graph of the function and complete the ordered pairs $(0,1)$ and $(1$ , $) .$ - $f(x)=7^{0.4 x}$

Find the value of the expression. - $\log _{4} \frac{1}{4}$

Classify the function as a linear, quadratic, or exponential. - $f(x)=-x$

Solve the equation. - $\log x^{2}=(\log x)^{2}$

Evaluate the expression. - $\log _{41} 97.52$

Convert to exponential form. - $\log _{4} 64=3$

Write the logarithmic and exponential equations associated with the display. - $f(x)=\log x$ $Write the logarithmic and exponential equations associated with the display. - f(x)=\log x$

Solve the equation. - $2 \mathrm{e}^{2 \mathrm{x}-5}=10$

Solve the problem. -The decay of $289 \mathrm{mg}$ of an isotope is given by $A(t)=289 e^{-0.027 t}$ , where $t$ is time in years. Find the amount left after 4 years.

Solve the equation for $s$ . - $\log (4+r)=\log (3 s-2)$

Graph the function. - $y=\log _{5}(x-1)$ $Graph the function. - y=\log _{5}(x-1)$

Graph the function. - $f(x)=3^{-x}$ $Graph the function. - f(x)=3^{-x}$

Graph the function. - $f(x)=2(x-2)$

Provide an appropriate response. -Can you solve this equation without using logarithms? 5 = 3^x Why or why not?