Question 1

Use a calculator to evaluate the logarithm.
-$\ln 96$

Accepted Answer

A)  1.9823 
B)  4.5643 
C)  35.4244 
D)  0.2184 
A)  1.9823 
B)  4.5643 
C)  35.4244 
D)  0.2184

Question 2

Express the following in terms of $u$ and $v$, where $u=\ln x$ and $v=\ln y$. For example, $\ln x=3(\ln x)=3 u$.
-$\ln \left(\frac{y^{7}}{x^{13}}\right)$

Accepted Answer

A)  $7 u-13 v$ 
B)  $\frac{v^{7}}{u^{13}}$ 
C)  $\frac{7 v}{13 u}$ 
D)  $7 v-13 u$ 
A)  $7 u-13 v$ 
B)  $\frac{v^{7}}{u^{13}}$ 
C)  $\frac{7 v}{13 u}$ 
D)  $7 v-13 u$

Question 3

Find the value of the expression.
-ln e

Accepted Answer

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

Question 4

Solve the problem.
-The number of books in a small library increases according to the function $B=8700 e^{0.04 t}$, where $t$ is measured in years. How many books will the library have after 7 years?

Accepted Answer

A)  11,511 
B)  11,075 
C)  4810 
D)  16,578 
A)  11,511 
B)  11,075 
C)  4810 
D)  16,578

Question 5

Solve the problem.
-A certain radioactive isotope decays at a rate of $0.15 \%$ annually. Determine the half-life of this isotope, to the nearest year.

Accepted Answer

A)  333 years 
B)  5 years 
C)  201 years 
D)  462 years 
A)  333 years 
B)  5 years 
C)  201 years 
D)  462 years

Question 6

without graphing, describe the shape of the graph of the function and complete the ordered pairs $(0,1)$ and $(1$,$) .$
-$f(x)=4^{2 x}$

Accepted Answer

A)  The graph lies below the $x$-axis, falls from right to left, with the positive $x$-axis as a horizontal asymptote; $(0,4)$ and $(1,16)$. 
B)  The graph lies above the $x$-axis, rises from right to left, with the negative $x$-axis as a horizontal asymptote; $(0,4)$ and $(1,16)$. 
C)  The graph lies above the $x$-axis, rises from left to right, with the negative $x$-axis as a horizontal asymptote; $(0,4)$ and $(1,16)$. 
D)  The graph lies below the $x$-axis, falls from left to right, with the positive $x$-axis as a horizontal asymptote; $(0,1)$ and $(1,-16)$. 
A)  The graph lies below the $x$-axis, falls from right to left, with the positive $x$-axis as a horizontal asymptote; $(0,4)$ and $(1,16)$. 
B)  The graph lies above the $x$-axis, rises from right to left, with the negative $x$-axis as a horizontal asymptote; $(0,4)$ and $(1,16)$. 
C)  The graph lies above the $x$-axis, rises from left to right, with the negative $x$-axis as a horizontal asymptote; $(0,4)$ and $(1,16)$. 
D)  The graph lies below the $x$-axis, falls from left to right, with the positive $x$-axis as a horizontal asymptote; $(0,1)$ and $(1,-16)$.

Question 7

Graph the function.
-$f(x)=4^{x}$

Accepted Answer

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

Question 8

Solve the problem.
-The number of books in a small library increases according to the function $B=3700 \mathrm{e}^{0.05 t}$, where $t$ is measured in years. How many books will the library have after 3 years?

Accepted Answer

A)  5226 
B)  4299 
C)  3048 
D)  7019 
A)  5226 
B)  4299 
C)  3048 
D)  7019

Question 9

Solve the equation.
-$6^{\mathrm{x}+1}=29$

Accepted Answer

A)  2.879 
B)  5.033 
C)  1.879 
D)  0.879 
A)  2.879 
B)  5.033 
C)  1.879 
D)  0.879

Question 10

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

Accepted Answer

A)  $\ln 2.25=0.35218251811 ; \mathrm{e}^{0.35218251811}=2.25$ 
B)  $\ln 0.35218251811=2.25 ; \mathrm{e}^{2.25}=0.35218251811$ 
C)  $\ln 0.81093021622=2.25 ; \mathrm{e}^{2.25}=0.81093021622$ 
D)  $\ln 2.25=0.81093021622 ; \mathrm{e}^{0.81093021622}=2.25$ 
A)  $\ln 2.25=0.35218251811 ; \mathrm{e}^{0.35218251811}=2.25$ 
B)  $\ln 0.35218251811=2.25 ; \mathrm{e}^{2.25}=0.35218251811$ 
C)  $\ln 0.81093021622=2.25 ; \mathrm{e}^{2.25}=0.81093021622$ 
D)  $\ln 2.25=0.81093021622 ; \mathrm{e}^{0.81093021622}=2.25$

Question 11

Solve the problem.
-A certain noise measures 113 decibels. If the intensity is multiplied by 10 , how many decibels will the new noise measure? Use the formula $\mathrm{D}=10 \log \left(\mathrm{S} / \mathrm{S}_{0}\right)$, where $\mathrm{S}_{0}=10^{-12} \mathrm{watt} / \mathrm{m}^{2}$.

Accepted Answer

A)  123 decibels 
B)  114 decibels 
C)  1130 decibels 
D)  113 decibels 
A)  123 decibels 
B)  114 decibels 
C)  1130 decibels 
D)  113 decibels

Question 12

Solve the problem.
-The number of years since two independently evolving languages split off from a common ancestral language is approximated by $N(r)=-5000 \ln r$, where $r$ is the percent of words from the ancestral language common to both languages now. Find $r$ if two languages split about 1530 years ago. Round to the nearest percent.

Accepted Answer

A)  $74 \%$ 
B)  $153 \%$ 
C)  $7 \%$ 
D)  $15 \%$ 
A)  $74 \%$ 
B)  $153 \%$ 
C)  $7 \%$ 
D)  $15 \%$

Question 13

Solve.
-In recent years, many states have passed laws against smoking in public buildings. The total number of states $\mathrm{N}$ that have passed a no smoking in public buildings law, $\mathrm{t}$ years after 1985 is given by the function
$\mathrm{N}(\mathrm{t})=\frac{50}{1+19 \mathrm{e}^{-0.4 \mathrm{t}}}$
How many states had passed the law in 1985 ?

Accepted Answer

A)  2.5 
B)  1.25 
C)  0.25 
D)  0 
A)  2.5 
B)  1.25 
C)  0.25 
D)  0

Question 14

Write the expression as a sum and/or a difference of logarithms with all variables to the first degree.
-$\ln \frac{\sqrt{\mathrm{fz}}}{\mathrm{z}^{9}}$

Accepted Answer

A)  $\ln \mathrm{f}-\frac{17}{2} \ln \mathrm{z}$ 
B)  $\ln f-9 \ln z$ 
C)  $\frac{1}{2} \ln \mathrm{f}-\frac{17}{2} \ln \mathrm{z}$ 
D)  $\frac{1}{2} \ln \mathrm{fz}-9 \ln \mathrm{z}$ 
A)  $\ln \mathrm{f}-\frac{17}{2} \ln \mathrm{z}$ 
B)  $\ln f-9 \ln z$ 
C)  $\frac{1}{2} \ln \mathrm{f}-\frac{17}{2} \ln \mathrm{z}$ 
D)  $\frac{1}{2} \ln \mathrm{fz}-9 \ln \mathrm{z}$

Question 15

Convert to exponential form.
-$\log _{5} 125=3$

Accepted Answer

A)  $(3)^{5}=125$ 
B)  $(5)^{125}=3$ 
C)  $(125)^{3}=5$ 
D)  $(5)^{3}=125$ 
A)  $(3)^{5}=125$ 
B)  $(5)^{125}=3$ 
C)  $(125)^{3}=5$ 
D)  $(5)^{3}=125$

Question 16

Classify the function as a linear, quadratic, or exponential.
-$f(x)=-6 x^{2}-5 x-6$

Accepted Answer

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

Question 17

Solve the problem.
-The height in meters of women of a certain tribe is approximated by $h=0.52+2 \log (t / 3)$ where $t$ is the woman's age in years and $1 \leq t \leq 20$. Estimate the height (to the nearest hundredth of a meter) of a woman of the tribe 4 years of age.

Accepted Answer

A)  $0.96 \mathrm{~m}$ 
B)  $0.52 \mathrm{~m}$ 
C)  $0.77 \mathrm{~m}$ 
D)  $1.12 \mathrm{~m}$ 
A)  $0.96 \mathrm{~m}$ 
B)  $0.52 \mathrm{~m}$ 
C)  $0.77 \mathrm{~m}$ 
D)  $1.12 \mathrm{~m}$

Question 18

Use a calculator to evaluate the logarithm.
-$\log 4174$

Accepted Answer

A)  8.3366 
B)  3.6216 
C)  3.6195 
D)  3.6206 
A)  8.3366 
B)  3.6216 
C)  3.6195 
D)  3.6206

Question 19

Solve the equation.
-$\log 5 x=\log 3+\log (x-4)$

Accepted Answer

A)  $-\frac{3}{2}$ 
B)  $-\frac{1}{4}$ 
C)  6 
D)  -6 
A)  $-\frac{3}{2}$ 
B)  $-\frac{1}{4}$ 
C)  6 
D)  -6

Question 20

Provide an appropriate response.
-In your own words, explain what a logarithm is.

Accepted Answer

Loga^x is the exponent

Use a calculator to evaluate the logarithm. - $\ln 96$

Express the following in terms of $u$ and $v$ , where $u=\ln x$ and $v=\ln y$ . For example, $\ln x=3(\ln x)=3 u$ . - $\ln \left(\frac{y^{7}}{x^{13}}\right)$

Find the value of the expression. -ln e

Solve the problem. -The number of books in a small library increases according to the function $B=8700 e^{0.04 t}$ , where $t$ is measured in years. How many books will the library have after 7 years?

Solve the problem. -A certain radioactive isotope decays at a rate of $0.15 \%$ annually. Determine the half-life of this isotope, to the nearest year.

without graphing, describe the shape of the graph of the function and complete the ordered pairs $(0,1)$ and $(1$ , $) .$ - $f(x)=4^{2 x}$

Graph the function. - $f(x)=4^{x}$ $Graph the function. - f(x)=4^{x}$

Solve the problem. -The number of books in a small library increases according to the function $B=3700 \mathrm{e}^{0.05 t}$ , where $t$ is measured in years. How many books will the library have after 3 years?

Solve the equation. - $6^{\mathrm{x}+1}=29$

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

Solve the problem. -A certain noise measures 113 decibels. If the intensity is multiplied by 10 , how many decibels will the new noise measure? Use the formula $\mathrm{D}=10 \log \left(\mathrm{S} / \mathrm{S}_{0}\right)$ , where $\mathrm{S}_{0}=10^{-12} \mathrm{watt} / \mathrm{m}^{2}$ .

Write the expression as a sum and/or a difference of logarithms with all variables to the first degree. - $\ln \frac{\sqrt{\mathrm{fz}}}{\mathrm{z}^{9}}$

Convert to exponential form. - $\log _{5} 125=3$

Classify the function as a linear, quadratic, or exponential. - $f(x)=-6 x^{2}-5 x-6$

Solve the problem. -The height in meters of women of a certain tribe is approximated by $h=0.52+2 \log (t / 3)$ where $t$ is the woman's age in years and $1 \leq t \leq 20$ . Estimate the height (to the nearest hundredth of a meter) of a woman of the tribe 4 years of age.

Use a calculator to evaluate the logarithm. - $\log 4174$

Solve the equation. - $\log 5 x=\log 3+\log (x-4)$

Provide an appropriate response. -In your own words, explain what a logarithm is.

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

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Exam 4: Exponential and Logarithmic Functions

Use a calculator to evaluate the logarithm. - ln⁡96\ln 96ln96

Express the following in terms of uuu and vvv , where u=ln⁡xu=\ln xu=lnx and v=ln⁡yv=\ln yv=lny . For example, ln⁡x=3(ln⁡x)=3u\ln x=3(\ln x)=3 ulnx=3(lnx)=3u . - ln⁡(y7x13)\ln \left(\frac{y^{7}}{x^{13}}\right)ln(x13y7​)