Question 1

By what order of magnitude do the numbers 0.000001 and $100,000,000$ differ?

Accepted Answer

The answer of By what order of magnitude do the...

Question 2

Use linear regression on the values $\mathrm{x}$ and $\ln y$ to fit a function of the form $\ln y=b+m x$.
   
Use a calculator program to find the vertical intercept of the regression line for this data. Round to 4 decimal places.

Accepted Answer

The answer of Use linear regression on the values $\mathrm{x}$...

Question 3

Suppose a certain population decreases by one third every 4 years. If the population is initially 17,000 , what is the size of the population after 10 years? Round your answer to the nearest whole number.

Accepted Answer

The answer of Suppose a certain population decreases by one...

Question 4

The following table gives $v$ as a linear function of $w$.
 
If $w=\ln x$ and $v=\ln y$, which of the following is a formula for $y$ in terms of $x$ ?

Accepted Answer

A)  $y=3 x$ 
B)  $y=\ln (3 x)$ 
C)  $y=x^{3}$ 
D)  $y=e^{3 x}$ 
A)  $y=3 x$ 
B)  $y=\ln (3 x)$ 
C)  $y=x^{3}$ 
D)  $y=e^{3 x}$

Question 5

The half-life of a substance is 37 hours. If there are initially 145 grams of the substance, how many grams are remaining after 52 hours? Round your answer to 3 decimal places.

Accepted Answer

The answer of The half-life of a substance is 37...

Question 6

What annual interest rate, compounded quarterly, is equivalent to an annual interest rate of $5.5 \%$ compounded continuously? Round your answer to the nearest thousandth of a percent, if necessary.

Accepted Answer

The answer of What annual interest rate, compounded quarterly, is...

Question 7

Find the domain of the function $f(x)=\sqrt{-5 \ln (x-5)}-6$.

Accepted Answer

The answer of Find the domain of the function \(f(x)=\sqrt{-5...

Question 8

Sound A is $32 \mathrm{~dB}$. Sound B is $54 \mathrm{~dB}$. How many times more intense is Sound $B$ than Sound A? Round your answer to 2 decimal places if necessary.

Accepted Answer

Sound B is 158.49 ti

Question 9

The following table gives $v$ as a linear function of $w$.
   
If $w=\ln x, v=\ln u$, and $u=\ln y$, find a formula for $y$ in terms of $x$.

Accepted Answer

The answer of The following table gives $v$ as a...

Question 10

Find the domain and asymptotes of the function $f(x)=-4\left[\ln \left(x^{2}-4\right)-\ln (x+2)\right]$

Accepted Answer

Domain : All real nu

Question 11

Evaluate $e^{\ln 9}$

Accepted Answer

The answer of Evaluate $e^{\ln 9}$...

Question 12

The following table gives $z$ as a linear function of $x$.
   
If $z=\ln y$, find a formula for $y$ in terms of $x$.

Accepted Answer

The answer of The following table gives $z$ as a...

Question 13

Solve $\frac{1}{12}=\left(\frac{1}{6}\right)^{x}$ using logs. Give your answer to 3 decimal places.

Accepted Answer

The answer of Solve $\frac{1}{12}=\left(\frac{1}{6}\right)^{x}$ using logs. Give your answer...

Question 14

What is the range of the function $y=\ln (x-6)$ ?

Accepted Answer

The answer of What is the range of the function...

Question 15

Does $\frac{\log A^{4}-\log \sqrt{A}}{\log \left(e^{\ln e}\right)}=\frac{7}{2} \frac{\log A}{\log e}$ ?

Accepted Answer

A) True 
 B)False

Question 16

Solve for $t: \log (t-500)=4$

Accepted Answer

The answer of Solve for $t: \log (t-500)=4$...

Question 17

The hydrogen ion concentration $\left[\mathrm{H}^{+}\right]$for a certain substance is 0.000316 . What is the $\mathrm{pH}$ of the substance?

Accepted Answer

The answer of The hydrogen ion concentration $\left[\mathrm{H}^{+}\right]$for a certain...

Question 18

Use linear regression on the values $x$ and $\ln y$ to fit a function of the form $\ln y=b+m x$.
   
Use a calculator program to find the regression line for this data. Convert to an exponential function $y=a e^{k x}$. Give the value of $k$. Round to 4 decimal places.

Accepted Answer

The answer of Use linear regression on the values $x$...

Question 19

The following table gives $z$ as a linear function of $x$.
 
If $z=\ln y$, which of the following is a formula for $y$ in terms of $x$ ?

Accepted Answer

A)  $y=\ln (-1+3 x)$ 
B)  $y=e^{-1+3 x}$ 
C)  $y=-1 \ln (3 x)$ 
D)  $y=-1 e^{3 x}$ 
A)  $y=\ln (-1+3 x)$ 
B)  $y=e^{-1+3 x}$ 
C)  $y=-1 \ln (3 x)$ 
D)  $y=-1 e^{3 x}$

Question 20

The vertical asymptote of the graph of $y=5+\ln (4-x)$ is at $x=$----------- Round to 2 decimal places if necessary.

Accepted Answer

The answer of The vertical asymptote of the graph of...

By what order of magnitude do the numbers 0.000001 and $100,000,000$ differ?

Suppose a certain population decreases by one third every 4 years. If the population is initially 17,000 , what is the size of the population after 10 years? Round your answer to the nearest whole number.

The following table gives $v$ as a linear function of $w$ . $The following table gives v as a linear function of w . If w=\ln x and v=\ln y , which of the following is a formula for y in terms of x ?$ If $w=\ln x$ and $v=\ln y$ , which of the following is a formula for $y$ in terms of $x$ ?

The half-life of a substance is 37 hours. If there are initially 145 grams of the substance, how many grams are remaining after 52 hours? Round your answer to 3 decimal places.

What annual interest rate, compounded quarterly, is equivalent to an annual interest rate of $5.5 \%$ compounded continuously? Round your answer to the nearest thousandth of a percent, if necessary.

Find the domain of the function $f(x)=\sqrt{-5 \ln (x-5)}-6$ .

Sound A is $32 \mathrm{~dB}$ . Sound B is $54 \mathrm{~dB}$ . How many times more intense is Sound $B$ than Sound A? Round your answer to 2 decimal places if necessary.

The following table gives $v$ as a linear function of $w$ . $The following table gives v as a linear function of w . If w=\ln x, v=\ln u , and u=\ln y , find a formula for y in terms of x .$ If $w=\ln x, v=\ln u$ , and $u=\ln y$ , find a formula for $y$ in terms of $x$ .

Find the domain and asymptotes of the function $f(x)=-4\left[\ln \left(x^{2}-4\right)-\ln (x+2)\right]$

Evaluate $e^{\ln 9}$

The following table gives $z$ as a linear function of $x$ . $The following table gives z as a linear function of x . If z=\ln y , find a formula for y in terms of x .$ If $z=\ln y$ , find a formula for $y$ in terms of $x$ .

Solve $\frac{1}{12}=\left(\frac{1}{6}\right)^{x}$ using logs. Give your answer to 3 decimal places.

What is the range of the function $y=\ln (x-6)$ ?

Does $\frac{\log A^{4}-\log \sqrt{A}}{\log \left(e^{\ln e}\right)}=\frac{7}{2} \frac{\log A}{\log e}$ ?

Solve for $t: \log (t-500)=4$

The hydrogen ion concentration $\left[\mathrm{H}^{+}\right]$ for a certain substance is 0.000316 . What is the $\mathrm{pH}$ of the substance?

The following table gives $z$ as a linear function of $x$ . $The following table gives z as a linear function of x . If z=\ln y , which of the following is a formula for y in terms of x ?$ If $z=\ln y$ , which of the following is a formula for $y$ in terms of $x$ ?

The vertical asymptote of the graph of $y=5+\ln (4-x)$ is at $x=$ ----------- Round to 2 decimal places if necessary.

Linear Functions and Change

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Quadratic Functions

Exponential Functions

Transformations of Functions and Their Graphs

Trigonometry and Periodic Functions

Triangle Trigonometry and Polar Coordinates

Trigonometric Identities, Models, and Complex Numbers

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Exam 5: Logarithmic Functions

By what order of magnitude do the numbers 0.000001 and 100,000,000100,000,000100,000,000 differ?

Use linear regression on the values x\mathrm{x}x and ln⁡y\ln ylny to fit a function of the form ln⁡y=b+mx\ln y=b+m xlny=b+mx . Use a calculator program to find the vertical intercept of the regression line for this data. Round to 4 decimal places.

Suppose a certain population decreases by one third every 4 years. If the population is initially 17,000 , what is the size of the population after 10 years? Round your answer to the nearest whole number.

The following table gives vvv as a linear function of www . If w=ln⁡xw=\ln xw=lnx and v=ln⁡yv=\ln yv=lny , which of the following is a formula for yyy in terms of xxx ?

The half-life of a substance is 37 hours. If there are initially 145 grams of the substance, how many grams are remaining after 52 hours? Round your answer to 3 decimal places.

What annual interest rate, compounded quarterly, is equivalent to an annual interest rate of 5.5%5.5 \%5.5% compounded continuously? Round your answer to the nearest thousandth of a percent, if necessary.

Find the domain of the function f(x)=−5ln⁡(x−5)−6f(x)=\sqrt{-5 \ln (x-5)}-6f(x)=−5ln(x−5)​−6 .

Sound A is 32 dB32 \mathrm{~dB}32 dB . Sound B is 54 dB54 \mathrm{~dB}54 dB . How many times more intense is Sound BBB than Sound A? Round your answer to 2 decimal places if necessary.

The following table gives vvv as a linear function of www . If w=ln⁡x,v=ln⁡uw=\ln x, v=\ln uw=lnx,v=lnu , and u=ln⁡yu=\ln yu=lny , find a formula for yyy in terms of xxx .

Find the domain and asymptotes of the function f(x)=−4[ln⁡(x2−4)−ln⁡(x+2)]f(x)=-4\left[\ln \left(x^{2}-4\right)-\ln (x+2)\right]f(x)=−4[ln(x2−4)−ln(x+2)]

Evaluate eln⁡9e^{\ln 9}eln9

The following table gives zzz as a linear function of xxx . If z=ln⁡yz=\ln yz=lny , find a formula for yyy in terms of xxx .

Solve 112=(16)x\frac{1}{12}=\left(\frac{1}{6}\right)^{x}121​=(61​)x using logs. Give your answer to 3 decimal places.

What is the range of the function y=ln⁡(x−6)y=\ln (x-6)y=ln(x−6) ?

Does log⁡A4−log⁡Alog⁡(eln⁡e)=72log⁡Alog⁡e\frac{\log A^{4}-\log \sqrt{A}}{\log \left(e^{\ln e}\right)}=\frac{7}{2} \frac{\log A}{\log e}log(elne)logA4−logA​​=27​logelogA​ ?

Solve for t:log⁡(t−500)=4t: \log (t-500)=4t:log(t−500)=4

The hydrogen ion concentration [H+]\left[\mathrm{H}^{+}\right][H+] for a certain substance is 0.000316 . What is the pH\mathrm{pH}pH of the substance?

The following table gives zzz as a linear function of xxx . If z=ln⁡yz=\ln yz=lny , which of the following is a formula for yyy in terms of xxx ?

The vertical asymptote of the graph of y=5+ln⁡(4−x)y=5+\ln (4-x)y=5+ln(4−x) is at x=x=x= ----------- Round to 2 decimal places if necessary.

Linear Functions and Change

Functions

Quadratic Functions

Exponential Functions

Transformations of Functions and Their Graphs

Trigonometry and Periodic Functions

Triangle Trigonometry and Polar Coordinates

Trigonometric Identities, Models, and Complex Numbers

Compositions, Inverses, and Combinations of Functions

Polynomial and Rational Functions

Vectors and Matrices

Sequences and Series

Parametric Equations and Conic Sections

Filters

By what order of magnitude do the numbers 0.000001 and $100,000,000$ differ?

The following table gives $v$ as a linear function of $w$ . $The following table gives v as a linear function of w . If w=\ln x and v=\ln y , which of the following is a formula for y in terms of x ?$ If $w=\ln x$ and $v=\ln y$ , which of the following is a formula for $y$ in terms of $x$ ?

What annual interest rate, compounded quarterly, is equivalent to an annual interest rate of $5.5 \%$ compounded continuously? Round your answer to the nearest thousandth of a percent, if necessary.

Find the domain of the function $f(x)=\sqrt{-5 \ln (x-5)}-6$ .

Sound A is $32 \mathrm{~dB}$ . Sound B is $54 \mathrm{~dB}$ . How many times more intense is Sound $B$ than Sound A? Round your answer to 2 decimal places if necessary.

The following table gives $v$ as a linear function of $w$ . $The following table gives v as a linear function of w . If w=\ln x, v=\ln u , and u=\ln y , find a formula for y in terms of x .$ If $w=\ln x, v=\ln u$ , and $u=\ln y$ , find a formula for $y$ in terms of $x$ .

Find the domain and asymptotes of the function $f(x)=-4\left[\ln \left(x^{2}-4\right)-\ln (x+2)\right]$

Evaluate $e^{\ln 9}$

The following table gives $z$ as a linear function of $x$ . $The following table gives z as a linear function of x . If z=\ln y , find a formula for y in terms of x .$ If $z=\ln y$ , find a formula for $y$ in terms of $x$ .

Solve $\frac{1}{12}=\left(\frac{1}{6}\right)^{x}$ using logs. Give your answer to 3 decimal places.

What is the range of the function $y=\ln (x-6)$ ?

Does $\frac{\log A^{4}-\log \sqrt{A}}{\log \left(e^{\ln e}\right)}=\frac{7}{2} \frac{\log A}{\log e}$ ?

Solve for $t: \log (t-500)=4$

The hydrogen ion concentration $\left[\mathrm{H}^{+}\right]$ for a certain substance is 0.000316 . What is the $\mathrm{pH}$ of the substance?

The following table gives $z$ as a linear function of $x$ . $The following table gives z as a linear function of x . If z=\ln y , which of the following is a formula for y in terms of x ?$ If $z=\ln y$ , which of the following is a formula for $y$ in terms of $x$ ?

The vertical asymptote of the graph of $y=5+\ln (4-x)$ is at $x=$ ----------- Round to 2 decimal places if necessary.