Question 1

Solve the problem.
-Use the data in the table to compute a logistic regression model for the population of the city t years after $1900 .$

Accepted Answer

A)  $\mathrm { P } ( \mathrm { t } ) = \frac { 11.679 } { 1 + 13.251 \mathrm { e } ^ { - 0.0116 \mathrm { t } } }$ 
B)  $\mathrm { P } ( \mathrm { t } ) = \frac { 10.279 } { 1 + 9.053 \mathrm { e } ^ { - 0.0273 \mathrm { t } } }$ 
C)  $\mathrm { P } ( \mathrm { t } ) = \frac { 8.731 } { 1 + 7.663 \mathrm { e } ^ { - 0.0362 \mathrm { t } } }$ 
D)  $\mathrm { P } ( \mathrm { t } ) = \frac { 9.053 } { 1 + 10.279 \mathrm { e } ^ { - 0.0273 \mathrm { t } } }$ 
A)  $\mathrm { P } ( \mathrm { t } ) = \frac { 11.679 } { 1 + 13.251 \mathrm { e } ^ { - 0.0116 \mathrm { t } } }$ 
B)  $\mathrm { P } ( \mathrm { t } ) = \frac { 10.279 } { 1 + 9.053 \mathrm { e } ^ { - 0.0273 \mathrm { t } } }$ 
C)  $\mathrm { P } ( \mathrm { t } ) = \frac { 8.731 } { 1 + 7.663 \mathrm { e } ^ { - 0.0362 \mathrm { t } } }$ 
D)  $\mathrm { P } ( \mathrm { t } ) = \frac { 9.053 } { 1 + 10.279 \mathrm { e } ^ { - 0.0273 \mathrm { t } } }$

Question 2

Solve the problem.
-The table shows the population of a certain city in various years. The data can be modeled by an exponential function of the form $f ( x ) = b a ^ { x }$. Use regression to determine an exponential function $f$ that models this data. Round the coefficients to the nearest hundredth.

Accepted Answer

A)  $\mathrm { f } ( \mathrm { x } ) = ( 14.21 ) ( 1.03 ) ^ { \mathrm { x } }$ 
B)  $f ( x ) = ( 0.62 ) ( 7.58 ) ^ { x }$ 
C)  $f ( x ) = ( 13.21 ) ( 1.03 ) ^ { x }$ 
D)  $f ( x ) = ( 7.58 ) ( 0.62 ) ^ { x }$ 
A)  $\mathrm { f } ( \mathrm { x } ) = ( 14.21 ) ( 1.03 ) ^ { \mathrm { x } }$ 
B)  $f ( x ) = ( 0.62 ) ( 7.58 ) ^ { x }$ 
C)  $f ( x ) = ( 13.21 ) ( 1.03 ) ^ { x }$ 
D)  $f ( x ) = ( 7.58 ) ( 0.62 ) ^ { x }$

Question 3

Describe how to transform the graph of the basic function g(x) into the graph of the given function f(x).
-$f ( x ) = - 5 \ln ( - x ) ; \quad g ( x ) = \ln x$

Accepted Answer

A)  Reflect across the $x$-axis and the $y$-axis and translate5 units down. 
B)  Reflect across the $y$-axis and vertically stretch by a factor of 5 . 
C)  Reflect across the $x$-axis and translate 5 units down. 
D)  Reflect across the $x$-axis and the $y$-axis and vertically stretch by a factor of 5 . 
A)  Reflect across the $x$-axis and the $y$-axis and translate5 units down. 
B)  Reflect across the $y$-axis and vertically stretch by a factor of 5 . 
C)  Reflect across the $x$-axis and translate 5 units down. 
D)  Reflect across the $x$-axis and the $y$-axis and vertically stretch by a factor of 5 .

Question 4

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, asymptotes, and end
behavior.
-f(x) = log1/2(4x)

Accepted Answer

@#IMG-DLM&
The domain is @#LAT-DLM&, and the range

Question 5

Find the amount accumulated after investing a principal P for t years at an interest rate r.
-P = $4307.17, t = 12 , r = 7% , compounded monthly (k = 12)

Accepted Answer

A)  $9952.67 
B)  $9904.76 
C)  $9700.57 
D)  $9834.68 
A)  $9952.67 
B)  $9904.76 
C)  $9700.57 
D)  $9834.68

Question 6

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, asymptotes, and end
behavior.
-f(x) = log3(x + 2)

Accepted Answer

@#IMG-DLM&
The domain is @#LAT-DLM&, and the range

Question 7

Find the exact solution to the equation.
-$$6 ^ { 7 x } = 36$$

Accepted Answer

A)  $x = \frac { 2 } { 7 }$ 
B)  $x = 64$ 
C)  $x = 36$ 
D)  $x = \frac { 7 } { 2 }$ 
A)  $x = \frac { 2 } { 7 }$ 
B)  $x = 64$ 
C)  $x = 36$ 
D)  $x = \frac { 7 } { 2 }$

Question 8

Write the expression using only the indicated logarithms.
-$\log 6 ( x + y )$ using common logarithms

Accepted Answer

A)  $\frac { \log 6 } { \log ( x + y ) }$ 
B)  $\frac { \log ( x + y ) } { \log 6 }$ 
C)  $\log ( x + y ) \log 6$ 
D)  $\log ( x + y ) + \log 6$ 
A)  $\frac { \log 6 } { \log ( x + y ) }$ 
B)  $\frac { \log ( x + y ) } { \log 6 }$ 
C)  $\log ( x + y ) \log 6$ 
D)  $\log ( x + y ) + \log 6$

Question 9

Provide an appropriate response.
-Use the change-of-base formula to explain how the graph of f(x) = log5 x can be obtained by applying a
transformation to the graph of g(x) = ln x.

Accepted Answer

By the change-of-bas

Question 10

Describe how to transform the graph of the basic function g(x) into the graph of the given function f(x).
-$$f ( x ) = 2 \log ( 4 - x ) ; \quad g ( x ) = \log x$$

Accepted Answer

A)  Reflect across the $y$-axis, translate 4 units to the right, and vertically stretch by a factor of 2 . 
B)  Reflect across the $y$-axis, translate 4 units to the left, and vertically stretch by a factor of 2 . 
C)  Reflect across the $x$-axis, translate 4 units to the left, and vertically stretch by a factor of 2 . 
D)  Reflect across the $x$-axis, translate 4 units to the right, and vertically stretch by a factor of 2 . 
A)  Reflect across the $y$-axis, translate 4 units to the right, and vertically stretch by a factor of 2 . 
B)  Reflect across the $y$-axis, translate 4 units to the left, and vertically stretch by a factor of 2 . 
C)  Reflect across the $x$-axis, translate 4 units to the left, and vertically stretch by a factor of 2 . 
D)  Reflect across the $x$-axis, translate 4 units to the right, and vertically stretch by a factor of 2 .

Question 11

Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all
variables represent positive real numbers.
-$\frac { 1 } { 3 } \ln x$

Accepted Answer

A)  $\ln \left( \frac { x } { 3 } \right)$ 
B)  $\ln ( \sqrt [ 3 ] { x } )$ 
C)  $\ln \left( x ^ { 3 } \right)$ 
D)  $\ln x - \ln 3$ 
A)  $\ln \left( \frac { x } { 3 } \right)$ 
B)  $\ln ( \sqrt [ 3 ] { x } )$ 
C)  $\ln \left( x ^ { 3 } \right)$ 
D)  $\ln x - \ln 3$

Question 12

Evaluate the logarithm.
-$\log _ { 5 } 625$

Accepted Answer

A)  5 
B)  20 
C)  625 
D)  4 
A)  5 
B)  20 
C)  625 
D)  4

Question 13

Graph the function. Describe its position relative to the graph of the indicated basic function.
-$$f ( x ) = \frac { 1 } { 5 } \ln x \text {; relative to } f ( x ) = \ln x$$

Accepted Answer

A)  Stretched vertically
  
B)  Shrunk vertically
  
C)  Shrunk horizontally
  
D)  Moved down 5 units
  
A)  Stretched vertically
  
B)  Shrunk vertically
  
C)  Shrunk horizontally
  
D)  Moved down 5 units

Question 14

Use the change of base rule to find the logarithm to four decimal places.
-$\log _ { 2 } 99.13$

Accepted Answer

A)  $0.1508$ 
B)  $6.6312$ 
C)  $1.9962$ 
D)  $49.5650$ 
A)  $0.1508$ 
B)  $6.6312$ 
C)  $1.9962$ 
D)  $49.5650$

Question 15

Solve the problem.
-The number of students infected with the flu on a college campus after $t$ days is modeled by the function $P ( t ) = \frac { 600 } { 1 + 39 e ^ { - 0.3 t } }$. What is the maximum number of infected students possible?

Accepted Answer

A)  300 
B)  15 
C)  1200 
D)  600 
A)  300 
B)  15 
C)  1200 
D)  600

Question 16

Determine the doubling time of the investment.
-6% APR compounded annually

Accepted Answer

A)  17.84 years 
B)  9.52 years 
C)  11.9 years 
D)  23.79 years 
A)  17.84 years 
B)  9.52 years 
C)  11.9 years 
D)  23.79 years

Question 17

Simplify the expression.
-$10 ^ { \log 5 }$

Accepted Answer

A)  $10 ^ { 5 }$ 
B)  $\frac { 1 } { 5 }$ 
C)  $\log 5$ 
D)  5 
A)  $10 ^ { 5 }$ 
B)  $\frac { 1 } { 5 }$ 
C)  $\log 5$ 
D)  5

Question 18

Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all
variables represent positive real numbers.
-$\frac { 2 } { 7 } \log _ { a } x + \frac { 1 } { 5 } \log _ { a } y$

Accepted Answer

A)  $\frac { 2 } { 35 } \log _ { a } x y$ 
B)  $\log _ { a } \left( x ^ { 2 / 7 } y ^ { 1 / 5 } \right)$ 
C)  $\log _ { a } \left( y ^ { 2 / 35 } \right)$ 
D)  $\log _ { a } \left( x y ^ { 2 / 35 } \right)$ 
A)  $\frac { 2 } { 35 } \log _ { a } x y$ 
B)  $\log _ { a } \left( x ^ { 2 / 7 } y ^ { 1 / 5 } \right)$ 
C)  $\log _ { a } \left( y ^ { 2 / 35 } \right)$ 
D)  $\log _ { a } \left( x y ^ { 2 / 35 } \right)$

Question 19

Find the following using a calculator. Round to four decimal places.
-ln (-11.4)

Accepted Answer

A)  undefined 
B)  2.4336 
C)  10.4 
D)  12.4 
A)  undefined 
B)  2.4336 
C)  10.4 
D)  12.4

Question 20

Determine the function which corresponds to the given graph.
- 
The asymptote is $x = 3$.

Accepted Answer

A)  $y = \ln ( x - 3 )$ 
B)  $y = \ln ( x + 3 )$ 
C)  $y = \ln x + 3$ 
D)  $y = \ln x - 3$ 
A)  $y = \ln ( x - 3 )$ 
B)  $y = \ln ( x + 3 )$ 
C)  $y = \ln x + 3$ 
D)  $y = \ln x - 3$

Solve the problem. -Use the data in the table to compute a logistic regression model for the population of the city t years after $1900 .$

Describe how to transform the graph of the basic function g(x) into the graph of the given function f(x). - $f ( x ) = - 5 \ln ( - x ) ; \quad g ( x ) = \ln x$

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, asymptotes, and end behavior. -f(x) = log1/2(4x)

Find the amount accumulated after investing a principal P for t years at an interest rate r. -P = $4307.17, t = 12 , r = 7% , compounded monthly (k = 12)

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, asymptotes, and end behavior. -f(x) = log3(x + 2)

Find the exact solution to the equation. - $6 ^ { 7 x } = 36$

Write the expression using only the indicated logarithms. - $\log 6 ( x + y )$ using common logarithms

Provide an appropriate response. -Use the change-of-base formula to explain how the graph of f(x) = log5 x can be obtained by applying a transformation to the graph of g(x) = ln x.

Describe how to transform the graph of the basic function g(x) into the graph of the given function f(x). - $f ( x ) = 2 \log ( 4 - x ) ; \quad g ( x ) = \log x$

Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all variables represent positive real numbers. - $\frac { 1 } { 3 } \ln x$

Evaluate the logarithm. - $\log _ { 5 } 625$

Use the change of base rule to find the logarithm to four decimal places. - $\log _ { 2 } 99.13$

Solve the problem. -The number of students infected with the flu on a college campus after $t$ days is modeled by the function $P ( t ) = \frac { 600 } { 1 + 39 e ^ { - 0.3 t } }$ . What is the maximum number of infected students possible?

Determine the doubling time of the investment. -6% APR compounded annually

Simplify the expression. - $10 ^ { \log 5 }$

Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all variables represent positive real numbers. - $\frac { 2 } { 7 } \log _ { a } x + \frac { 1 } { 5 } \log _ { a } y$

Find the following using a calculator. Round to four decimal places. -ln (-11.4)

Determine the function which corresponds to the given graph. - The asymptote is $x = 3$ .

Functions and Graphs

Polynomial, Power, and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 3: Exponential, Logistic, and Logarithmic Functions

Solve the problem. -Use the data in the table to compute a logistic regression model for the population of the city t years after 1900.1900 .1900.

Describe how to transform the graph of the basic function g(x) into the graph of the given function f(x). - f(x)=−5ln⁡(−x);g(x)=ln⁡xf ( x ) = - 5 \ln ( - x ) ; \quad g ( x ) = \ln xf(x)=−5ln(−x);g(x)=lnx