Question 1

Write in logarithmic form.
-$$4 ^ { 2 } = 16$$

Accepted Answer

A)  $\log _ { 4 } 2 = 16$ 
B)  $\log _ { 2 } 16 = 4$ 
C)  $\log _ { 4 } 16 = 2$ 
D)  $\log _ { 16 } 4 = 2$ 
A)  $\log _ { 4 } 2 = 16$ 
B)  $\log _ { 2 } 16 = 4$ 
C)  $\log _ { 4 } 16 = 2$ 
D)  $\log _ { 16 } 4 = 2$

Question 2

Provide an appropriate response.
-Give an example of a situation in which a logistic funct $f ( x ) = \frac { a } { 1 + b e ^ { - k x } }$ would be a more appropriate model
than an exponential function f(x) $f ( x ) = a e ^ { k x }$ . Explain why you think the logistic model would be more appropriate.

Accepted Answer

Population growth over a long period of

Question 3

Write the logarithmic equation in exponential form.
-$\log _ { 14 } 1 = 0$

Accepted Answer

A)  $14 ^ { 1 } = 0$ 
B)  $1 ^ { 14 } = 0$ 
C)  $0 ^ { 14 } = 1$ 
D)  $14 ^ { 0 } = 1$ 
A)  $14 ^ { 1 } = 0$ 
B)  $1 ^ { 14 } = 0$ 
C)  $0 ^ { 14 } = 1$ 
D)  $14 ^ { 0 } = 1$

Question 4

Wind speed varies in the first twenty meters above the ground. For a particular day, let  f(x)=1.2 ln x+8.5  model the wind speed  x  meters above the ground. What is the wind speed 8 meters above the ground? Round results to the nearest hundredth.

Accepted Answer

A)   11.07  meters per second 
B)   10.58  meters per second 
C)   11.00  meters per second 
D)   -6.00  meters per second 
A)   11.07  meters per second 
B)   10.58  meters per second 
C)   11.00  meters per second 
D)   -6.00  meters per second

Question 5

Find the function value.
-Let $f ( x ) = - 1.7 e ^ { - 0.8 x }$. Find $f ( - 1.6 )$, rounded to four decimal places.

Accepted Answer

A)  $- 0.4727$ 
B)  -6.1143 
C)  $0.4727$ 
D)  $6.1143$ 
A)  $- 0.4727$ 
B)  -6.1143 
C)  $0.4727$ 
D)  $6.1143$

Question 6

Write in logarithmic form.
-$$10 ^ { 3 } = 1000$$

Accepted Answer

A)  $\log _ { 3 } 10 = 1000$ 
B)  $\log _ { 3 } 1000 = 10$ 
C)  $\log _ { 10 } 3 = 1000$ 
D)  $\log _ { 10 } 1000 = 3$ 
A)  $\log _ { 3 } 10 = 1000$ 
B)  $\log _ { 3 } 1000 = 10$ 
C)  $\log _ { 10 } 3 = 1000$ 
D)  $\log _ { 10 } 1000 = 3$

Question 7

Explain the error in the following: $$\log _ { 6 } 8 - \log _ { 6 } \mathrm {~N} = \log _ { 6 } \left( 8 - \mathrm { N } ^ { 2 } \right.$$

Accepted Answer

A difference of loga

Question 8

Evaluate the logarithm, if possible. Round the answer to four decimal places.
-log 0.00474

Accepted Answer

A)  $- 5.3517$ 
B)  $- 2.3242$ 
C)  $- 2.3152$ 
D)  $- 2.3335$ 
A)  $- 5.3517$ 
B)  $- 2.3242$ 
C)  $- 2.3152$ 
D)  $- 2.3335$

Question 9

Use the properties of logarithms to evaluate the expression.
-$10 ^ { \log t }$

Accepted Answer

A)  $10 t$ 
B)  $10 ^ { t }$ 
C) 1 
D) t 
A)  $10 t$ 
B)  $10 ^ { t }$ 
C) 1 
D) t

Question 10

Explain how the graph of $y = - 4 \cdot 3 ^ { x } \text { can be obtained from the graph of } y = 3 ^ { x } \text {. }$

Accepted Answer

The graph is stretch

Question 11

A pharmaceutical company introduces a new headache medication on the market. They advertise the product on television and find that the percentage P of people who buy the product after t weeks satisfies the function $\mathrm { P } ( \mathrm { t } ) = \frac { 100 \% } { 1 + 37 \mathrm { e } ^ { - 0.13 \mathrm { t } } }$ What percentage buy the product after 16 weeks? Round to the nearest tenth of a percent
When necessary.

Accepted Answer

A)  17.8% 
B)  21.3% 
C)  14.2% 
D)  19.6% 
A)  17.8% 
B)  21.3% 
C)  14.2% 
D)  19.6%

Question 12

Provide an appropriate response.
-The function f $f ( x ) = 200 \frac { ( 1 + 0.06 / 4 ) ^ { x } - 1 } { 0.06 / 4 }$ describes the future value of a certain annuity. How many payments
per year are there?

Accepted Answer

There are

Question 13

$$\text { Given that } \log _ { a } 6 = 0.778 \text {, and } \log _ { a } 5 = 0.699 \text {, find } \log _ { a } 6 ^ { 2 } \text {. }$$

Accepted Answer

A)  0.544 
B)  1.477 
C)  0.605 
D)  1.556 
A)  0.544 
B)  1.477 
C)  0.605 
D)  1.556

Question 14

Match the equation with its graph.
-$y = 2 \cdot 2 ^ { x }$

Accepted Answer

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

Question 15

An artifact is discovered at a certain site. If it has 78% of the carbon-14 it originally contained, what is the approximate age of the artifact to the nearest year? Carbon-14 decays at the rate of 0.0125% annually. Round to
The nearest year, if necessary.

Accepted Answer

A)  6240 years 
B)  1760 years 
C)  863 years 
D)  1988 years 
A)  6240 years 
B)  1760 years 
C)  863 years 
D)  1988 years

Question 16

Rewrite the expression as the sum and/or difference of logarithms, without using exponents. Simplify if possible.
-$$\log _ { 2 } \frac { \sqrt [ 5 ] { m } \sqrt [ 9 ] { n } } { k ^ { 2 } }$$

Accepted Answer

A)  $5 \log _ { 2 } m + 9 \log _ { 2 } n - 2 \log _ { 2 } k$ 
B)  $\frac { 5 } { 2 } \log _ { 2 } \mathrm {~m} + \frac { 9 } { 2 } \log _ { 2 } \mathrm { n } - \frac { 1 } { 2 } \log _ { 2 } \mathrm { k }$ 
C)  $\frac { 1 } { 5 } \log _ { 2 } \mathrm {~m} \cdot \frac { 1 } { 9 } \log _ { 2 } \mathrm { n } \div 2 \log _ { 2 } \mathrm { k }$ 
D)  $\frac { 1 } { 5 } \log _ { 2 } \mathrm {~m} + \frac { 1 } { 9 } \log _ { 2 } \mathrm { n } - 2 \log _ { 2 } \mathrm { k }$ 
A)  $5 \log _ { 2 } m + 9 \log _ { 2 } n - 2 \log _ { 2 } k$ 
B)  $\frac { 5 } { 2 } \log _ { 2 } \mathrm {~m} + \frac { 9 } { 2 } \log _ { 2 } \mathrm { n } - \frac { 1 } { 2 } \log _ { 2 } \mathrm { k }$ 
C)  $\frac { 1 } { 5 } \log _ { 2 } \mathrm {~m} \cdot \frac { 1 } { 9 } \log _ { 2 } \mathrm { n } \div 2 \log _ { 2 } \mathrm { k }$ 
D)  $\frac { 1 } { 5 } \log _ { 2 } \mathrm {~m} + \frac { 1 } { 9 } \log _ { 2 } \mathrm { n } - 2 \log _ { 2 } \mathrm { k }$

Question 17

Find the amount of money in an account after 12 years if $4100 is deposited at 6% annual interest compounded quarterly.

Accepted Answer

A)  $8334.46 
B)  $8378.26 
C)  $8408.08 
D)  $8250.01 
A)  $8334.46 
B)  $8378.26 
C)  $8408.08 
D)  $8250.01

Question 18

In order to purchase a home, a family borrows $60,000 at an annual interest rate of 11%, to be paid back over a 30 year period in equal monthly payments. Find the total amount paid to the finance company for the life of the
Loan. Round your answer the nearest dollar.

Accepted Answer

A)  $198,000 
B)  $199,461 
C)  $201,934 
D)  $205,702 
A)  $198,000 
B)  $199,461 
C)  $201,934 
D)  $205,702

Question 19

Explain how the graph of $y = 4 ^ { x - 3 } + 2 \text { can be obtained from the graph of } y = 4 ^ { x }$ .

Accepted Answer

The graph is shifted

Question 20

Find the present value of a loan with an annual interest rate of 8.8% and periodic payments of $309.9 for a term of 5 years, with payments made and interest charged 12 times per year.

Accepted Answer

A)  $11,999.17 
B)  $29,997.93 
C)  $14,998.97 
D)  $26,998.14 
A)  $11,999.17 
B)  $29,997.93 
C)  $14,998.97 
D)  $26,998.14

Write in logarithmic form. - $4 ^ { 2 } = 16$

Write the logarithmic equation in exponential form. - $\log _ { 14 } 1 = 0$

Wind speed varies in the first twenty meters above the ground. For a particular day, let f(x)=1.2 ln x+8.5 model the wind speed x meters above the ground. What is the wind speed 8 meters above the ground? Round results to the nearest hundredth.

Find the function value. -Let $f ( x ) = - 1.7 e ^ { - 0.8 x }$ . Find $f ( - 1.6 )$ , rounded to four decimal places.

Write in logarithmic form. - $10 ^ { 3 } = 1000$

Explain the error in the following: $\log _ { 6 } 8 - \log _ { 6 } \mathrm {~N} = \log _ { 6 } \left( 8 - \mathrm { N } ^ { 2 } \right.$

Evaluate the logarithm, if possible. Round the answer to four decimal places. -log 0.00474

Use the properties of logarithms to evaluate the expression. - $10 ^ { \log t }$

Explain how the graph of $y = - 4 \cdot 3 ^ { x } \text { can be obtained from the graph of } y = 3 ^ { x } \text {. }$

Provide an appropriate response. -The function f $f ( x ) = 200 \frac { ( 1 + 0.06 / 4 ) ^ { x } - 1 } { 0.06 / 4 }$ describes the future value of a certain annuity. How many payments per year are there?

$\text { Given that } \log _ { a } 6 = 0.778 \text {, and } \log _ { a } 5 = 0.699 \text {, find } \log _ { a } 6 ^ { 2 } \text {. }$

Match the equation with its graph. - $y = 2 \cdot 2 ^ { x }$

An artifact is discovered at a certain site. If it has 78% of the carbon-14 it originally contained, what is the approximate age of the artifact to the nearest year? Carbon-14 decays at the rate of 0.0125% annually. Round to The nearest year, if necessary.

Rewrite the expression as the sum and/or difference of logarithms, without using exponents. Simplify if possible. - $\log _ { 2 } \frac { \sqrt [ 5 ] { m } \sqrt [ 9 ] { n } } { k ^ { 2 } }$

Find the amount of money in an account after 12 years if $4100 is deposited at 6% annual interest compounded quarterly.

In order to purchase a home, a family borrows $60,000 at an annual interest rate of 11%, to be paid back over a 30 year period in equal monthly payments. Find the total amount paid to the finance company for the life of the Loan. Round your answer the nearest dollar.

Explain how the graph of $y = 4 ^ { x - 3 } + 2 \text { can be obtained from the graph of } y = 4 ^ { x }$ .

Find the present value of a loan with an annual interest rate of 8.8% and periodic payments of $309.9 for a term of 5 years, with payments made and interest charged 12 times per year.

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Quadratic, Piecewise-Defined, and Power Functions

Additional Topics With Functions

Higher-Degree Polynomial and Rational Functions

Systems of Equations and Matrices

Special Topics in Algebra

Filters

Exam 5: Exponential and Logarithmic Functions

Write in logarithmic form. - 42=164 ^ { 2 } = 1642=16

Write the logarithmic equation in exponential form. - log⁡141=0\log _ { 14 } 1 = 0log14​1=0

Wind speed varies in the first twenty meters above the ground. For a particular day, let f(x)=1.2 ln x+8.5 model the wind speed x meters above the ground. What is the wind speed 8 meters above the ground? Round results to the nearest hundredth.

Find the function value. -Let f(x)=−1.7e−0.8xf ( x ) = - 1.7 e ^ { - 0.8 x }f(x)=−1.7e−0.8x . Find f(−1.6)f ( - 1.6 )f(−1.6) , rounded to four decimal places.

Write in logarithmic form. - 103=100010 ^ { 3 } = 1000103=1000

Explain the error in the following: log⁡68−log⁡6 N=log⁡6(8−N2\log _ { 6 } 8 - \log _ { 6 } \mathrm {~N} = \log _ { 6 } \left( 8 - \mathrm { N } ^ { 2 } \right.log6​8−log6​ N=log6​(8−N2

Evaluate the logarithm, if possible. Round the answer to four decimal places. -log 0.00474

Use the properties of logarithms to evaluate the expression. - 10log⁡t10 ^ { \log t }10logt

Explain how the graph of y=−4⋅3x can be obtained from the graph of y=3x. y = - 4 \cdot 3 ^ { x } \text { can be obtained from the graph of } y = 3 ^ { x } \text {. }y=−4⋅3x can be obtained from the graph of y=3x.

Provide an appropriate response. -The function f f(x)=200(1+0.06/4)x−10.06/4f ( x ) = 200 \frac { ( 1 + 0.06 / 4 ) ^ { x } - 1 } { 0.06 / 4 }f(x)=2000.06/4(1+0.06/4)x−1​ describes the future value of a certain annuity. How many payments per year are there?

Given that log⁡a6=0.778, and log⁡a5=0.699, find log⁡a62. \text { Given that } \log _ { a } 6 = 0.778 \text {, and } \log _ { a } 5 = 0.699 \text {, find } \log _ { a } 6 ^ { 2 } \text {. } Given that loga​6=0.778, and loga​5=0.699, find loga​62.

Match the equation with its graph. - y=2⋅2xy = 2 \cdot 2 ^ { x }y=2⋅2x

An artifact is discovered at a certain site. If it has 78% of the carbon-14 it originally contained, what is the approximate age of the artifact to the nearest year? Carbon-14 decays at the rate of 0.0125% annually. Round to The nearest year, if necessary.

Rewrite the expression as the sum and/or difference of logarithms, without using exponents. Simplify if possible. - log⁡2m5n9k2\log _ { 2 } \frac { \sqrt [ 5 ] { m } \sqrt [ 9 ] { n } } { k ^ { 2 } }log2​k25m​9n​​

Find the amount of money in an account after 12 years if $4100 is deposited at 6% annual interest compounded quarterly.

In order to purchase a home, a family borrows $60,000 at an annual interest rate of 11%, to be paid back over a 30 year period in equal monthly payments. Find the total amount paid to the finance company for the life of the Loan. Round your answer the nearest dollar.

Explain how the graph of y=4x−3+2 can be obtained from the graph of y=4xy = 4 ^ { x - 3 } + 2 \text { can be obtained from the graph of } y = 4 ^ { x }y=4x−3+2 can be obtained from the graph of y=4x .

Find the present value of a loan with an annual interest rate of 8.8% and periodic payments of $309.9 for a term of 5 years, with payments made and interest charged 12 times per year.

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Quadratic, Piecewise-Defined, and Power Functions

Additional Topics With Functions

Higher-Degree Polynomial and Rational Functions

Systems of Equations and Matrices

Special Topics in Algebra

Filters

Write in logarithmic form. - $4 ^ { 2 } = 16$

Write the logarithmic equation in exponential form. - $\log _ { 14 } 1 = 0$

Find the function value. -Let $f ( x ) = - 1.7 e ^ { - 0.8 x }$ . Find $f ( - 1.6 )$ , rounded to four decimal places.

Write in logarithmic form. - $10 ^ { 3 } = 1000$

Explain the error in the following: $\log _ { 6 } 8 - \log _ { 6 } \mathrm {~N} = \log _ { 6 } \left( 8 - \mathrm { N } ^ { 2 } \right.$

Use the properties of logarithms to evaluate the expression. - $10 ^ { \log t }$

Explain how the graph of $y = - 4 \cdot 3 ^ { x } \text { can be obtained from the graph of } y = 3 ^ { x } \text {. }$

Provide an appropriate response. -The function f $f ( x ) = 200 \frac { ( 1 + 0.06 / 4 ) ^ { x } - 1 } { 0.06 / 4 }$ describes the future value of a certain annuity. How many payments per year are there?

$\text { Given that } \log _ { a } 6 = 0.778 \text {, and } \log _ { a } 5 = 0.699 \text {, find } \log _ { a } 6 ^ { 2 } \text {. }$

Match the equation with its graph. - $y = 2 \cdot 2 ^ { x }$

Rewrite the expression as the sum and/or difference of logarithms, without using exponents. Simplify if possible. - $\log _ { 2 } \frac { \sqrt [ 5 ] { m } \sqrt [ 9 ] { n } } { k ^ { 2 } }$

Explain how the graph of $y = 4 ^ { x - 3 } + 2 \text { can be obtained from the graph of } y = 4 ^ { x }$ .