Question 1

Simplify the expression.
-$\mathrm { e } ^ { \ln ( 0.2 ) }$

Accepted Answer

A)  $- 0.2$ 
B)  $\ln ( 0.2 )$ 
C)  $e ^ { 0.2 }$ 
D)  $0.2$ 
A)  $- 0.2$ 
B)  $\ln ( 0.2 )$ 
C)  $e ^ { 0.2 }$ 
D)  $0.2$

Question 2

Determine a formula for the exponential function.
-

Accepted Answer

A)  $f ( x ) = \frac { 5 } { 3 } \cdot 3 ^ { x }$ 
B)  $f ( x ) = 5 \cdot 3 ^ { - x - 1 }$ 
C)  $f ( x ) = 5 \cdot \left( \frac { 1 } { 3 } \right) ^ { x }$ 
D)  $f ( x ) = 5 \cdot 3 ^ { - x }$ 
A)  $f ( x ) = \frac { 5 } { 3 } \cdot 3 ^ { x }$ 
B)  $f ( x ) = 5 \cdot 3 ^ { - x - 1 }$ 
C)  $f ( x ) = 5 \cdot \left( \frac { 1 } { 3 } \right) ^ { x }$ 
D)  $f ( x ) = 5 \cdot 3 ^ { - x }$

Question 3

Determine the function which corresponds to the given graph.
- 
The indicated point is $( 1 , - 5 )$.

Accepted Answer

A)  $y = \ln x - 5$ 
B)  $y = \ln ( x + 5 )$ 
C)  $y = \ln x + 5$ 
D)  $y = \ln ( x - 5 )$ 
A)  $y = \ln x - 5$ 
B)  $y = \ln ( x + 5 )$ 
C)  $y = \ln x + 5$ 
D)  $y = \ln ( x - 5 )$

Question 4

Compute the exact value of the function for the given x-value without using a calculator.
-$$f ( x ) = - 7 \cdot 11 ^ { x } \text { for } x = 1 / 4$$

Accepted Answer

A)  $- 11 \sqrt [ 4 ] { 7 }$ 
B)  $\frac { - 7 } { \sqrt [ 4 ] { 11 } }$ 
C)  $- \frac { 77 } { 4 }$ 
D)  $- 7 \sqrt [ 4 ] { 11 }$ 
A)  $- 11 \sqrt [ 4 ] { 7 }$ 
B)  $\frac { - 7 } { \sqrt [ 4 ] { 11 } }$ 
C)  $- \frac { 77 } { 4 }$ 
D)  $- 7 \sqrt [ 4 ] { 11 }$

Question 5

Assuming all variables are positive, use properties of logarithms to write the expression as a sum or difference of
logarithms or multiples of logarithms.
-$\log 9 x$

Accepted Answer

A)  $\log 9 \cdot \log x$ 
B)  $3 \log 2 + \log x$ 
C)  $2 \log 3 + \log x$ 
D)  $9 + \log x$ 
A)  $\log 9 \cdot \log x$ 
B)  $3 \log 2 + \log x$ 
C)  $2 \log 3 + \log x$ 
D)  $9 + \log x$

Question 6

Determine a formula for the exponential function.
-The graph of an exponential function is given. Which of the following is the correct equation of the function?

Accepted Answer

A)  $y = 0.65 x$ 
B)  $y = 2.4 ^ { x }$ 
C)  $y = 0.32 ^ { x }$ 
D)  $y = 3.5 ^ { x }$ 
A)  $y = 0.65 x$ 
B)  $y = 2.4 ^ { x }$ 
C)  $y = 0.32 ^ { x }$ 
D)  $y = 3.5 ^ { x }$

Question 7

Use a calculator to find an approximate solution to the equation.
-$e ^ { - 0.05 t } = 0.05$

Accepted Answer

A)  $59.9146$ 
B)  $49.9289$ 
C)  $- 74.8933$ 
D)  $- 59.9146$ 
A)  $59.9146$ 
B)  $49.9289$ 
C)  $- 74.8933$ 
D)  $- 59.9146$

Question 8

Solve the equation by changing it to exponential form.
-$\log _ { 9 } x = - 3$

Accepted Answer

A)  $x = - 9.3$ 
B)  $x = - ( 3 ) ^ { 9 }$ 
C)  $x = - \frac { 3 } { \log _ { 9 } 3 }$ 
D)  $x = \frac { 1 } { 9 ^ { 3 } }$ 
A)  $x = - 9.3$ 
B)  $x = - ( 3 ) ^ { 9 }$ 
C)  $x = - \frac { 3 } { \log _ { 9 } 3 }$ 
D)  $x = \frac { 1 } { 9 ^ { 3 } }$

Question 9

Choose the graph which matches the function.
-$$f ( x ) = 2 \cdot 0.7 ^ { 4 x }$$

Accepted Answer

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

Question 10

Determine the doubling time of the investment.
-$14,500 at 6% compounded monthly

Accepted Answer

A)  17.37 years 
B)  23.16 years 
C)  9.27 years 
D)  11.58 years 
A)  17.37 years 
B)  23.16 years 
C)  9.27 years 
D)  11.58 years

Question 11

Use a calculator to find an approximate solution to the equation.
-$( 3.5 ) ^ { x } = 47$

Accepted Answer

A)  $3.0856$ 
B)  $3.1967$ 
C)  $3.0733$ 
D)  $3.061$ 
A)  $3.0856$ 
B)  $3.1967$ 
C)  $3.0733$ 
D)  $3.061$

Question 12

Choose the graph which matches the function.
-$$f ( x ) = 5 ^ { - x }$$

Accepted Answer

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

Question 13

Solve the problem.
-Wind speed varies in the first twenty meters above the ground. For a particular day, let f(x) = 2.1 lnx + 3.1 compute the wind speed x meters above the ground. At what height is the wind speed 5 meters per second?
Round results to the nearest hundredth.

Accepted Answer

A)  2.46 m 
B)  0.40 m 
C)  0.90 m 
D)  1.22 m 
A)  2.46 m 
B)  0.40 m 
C)  0.90 m 
D)  1.22 m

Question 14

Find the logistic function that satisfies the given conditions.
-Initial height $= 169$, limit to growth $= 845$, passing through $( 2,585 )$

Accepted Answer

A)  $f ( x ) = \frac { 585 } { 1 + 4 \left( 1 / 9 ^ { x } \right. }$ 
B)  $f ( x ) = \frac { 845 } { 1 + 2 ( 1 / 3 ) ^ { x } }$ 
C)  $f ( x ) = \frac { 169 } { 1 + 3 ( 1 / 3 ) ^ { x } }$ 
D)  $f ( x ) = \frac { 845 } { 1 + 4 ( 1 / 3 ) ^ { x } }$ 
A)  $f ( x ) = \frac { 585 } { 1 + 4 \left( 1 / 9 ^ { x } \right. }$ 
B)  $f ( x ) = \frac { 845 } { 1 + 2 ( 1 / 3 ) ^ { x } }$ 
C)  $f ( x ) = \frac { 169 } { 1 + 3 ( 1 / 3 ) ^ { x } }$ 
D)  $f ( x ) = \frac { 845 } { 1 + 4 ( 1 / 3 ) ^ { x } }$

Question 15

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

Accepted Answer

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

Question 16

Compute the exact value of the function for the given x-value without using a calculator.
-$f ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x }$ for $x = 2$

Accepted Answer

A)  $\frac { 1 } { 9 }$ 
B)  $\frac { 1 } { 8 }$ 
C)  9 
D)  $\frac { 1 } { 6 }$ 
A)  $\frac { 1 } { 9 }$ 
B)  $\frac { 1 } { 8 }$ 
C)  9 
D)  $\frac { 1 } { 6 }$

Question 17

Solve the equation.
-$\log _ { 4 } ( 2 x + 5 ) - \log _ { 4 } ( x - 2 ) = 1$

Accepted Answer

A)  $3.125$ 
B)  $6.5$ 
C)  $2.408$ 
D)  No solution 
A)  $3.125$ 
B)  $6.5$ 
C)  $2.408$ 
D)  No solution

Question 18

Find the logistic function that satisfies the given conditions.
-Initial value $= 15$, limit to growth $= 60$, passing through $( 1,24 )$

Accepted Answer

A)  $f ( x ) = \frac { 24 } { 1 + 2 ( 1 / 3 ) ^ { x } }$ 
B)  $f ( x ) = \frac { 60 } { 1 + 3 ( 1 / 2 ) ^ { x } }$ 
C)  $f ( x ) = \frac { 15 } { 1 + 3 ( 1 / 2 ) ^ { x } }$ 
D)  $f ( x ) = \frac { 60 } { 1 + 2 ( 1 / 3 ) ^ { x } }$ 
A)  $f ( x ) = \frac { 24 } { 1 + 2 ( 1 / 3 ) ^ { x } }$ 
B)  $f ( x ) = \frac { 60 } { 1 + 3 ( 1 / 2 ) ^ { x } }$ 
C)  $f ( x ) = \frac { 15 } { 1 + 3 ( 1 / 2 ) ^ { x } }$ 
D)  $f ( x ) = \frac { 60 } { 1 + 2 ( 1 / 3 ) ^ { x } }$

Question 19

Solve the equation.
-$$\left( \frac { 1 } { 4 } \right) ^ { x } = 64$$

Accepted Answer

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

Question 20

Graph the function. Describe its position relative to the graph of the indicated basic function.
-$$f ( x ) = e ^ { - 0.9 x } ; \text { relative to } f ( x ) = e ^ { x }$$

Accepted Answer

A)  Stretched vertically;
reflected across the $y$-axis
  
B)  Stretched vertically 
  
C)  Stretched horizontally;
reflected across the $y$-axis
  
D)  Stretched horizontally 
  
A)  Stretched vertically;
reflected across the $y$-axis
  
B)  Stretched vertically 
  
C)  Stretched horizontally;
reflected across the $y$-axis
  
D)  Stretched horizontally

Simplify the expression. - $\mathrm { e } ^ { \ln ( 0.2 ) }$

Determine a formula for the exponential function. -

Determine the function which corresponds to the given graph. - The indicated point is $( 1 , - 5 )$ .

Compute the exact value of the function for the given x-value without using a calculator. - $f ( x ) = - 7 \cdot 11 ^ { x } \text { for } x = 1 / 4$

Assuming all variables are positive, use properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. - $\log 9 x$

Determine a formula for the exponential function. -The graph of an exponential function is given. Which of the following is the correct equation of the function?

Use a calculator to find an approximate solution to the equation. - $e ^ { - 0.05 t } = 0.05$

Solve the equation by changing it to exponential form. - $\log _ { 9 } x = - 3$

Choose the graph which matches the function. - $f ( x ) = 2 \cdot 0.7 ^ { 4 x }$ $Choose the graph which matches the function. - f ( x ) = 2 \cdot 0.7 ^ { 4 x }$

Determine the doubling time of the investment. -$14,500 at 6% compounded monthly

Use a calculator to find an approximate solution to the equation. - $( 3.5 ) ^ { x } = 47$

Choose the graph which matches the function. - $f ( x ) = 5 ^ { - x }$ $Choose the graph which matches the function. - f ( x ) = 5 ^ { - x }$

Solve the problem. -Wind speed varies in the first twenty meters above the ground. For a particular day, let f(x) = 2.1 lnx + 3.1 compute the wind speed x meters above the ground. At what height is the wind speed 5 meters per second? Round results to the nearest hundredth.

Find the logistic function that satisfies the given conditions. -Initial height $= 169$ , limit to growth $= 845$ , passing through $( 2,585 )$

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

Compute the exact value of the function for the given x-value without using a calculator. - $f ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x }$ for $x = 2$

Solve the equation. - $\log _ { 4 } ( 2 x + 5 ) - \log _ { 4 } ( x - 2 ) = 1$

Find the logistic function that satisfies the given conditions. -Initial value $= 15$ , limit to growth $= 60$ , passing through $( 1,24 )$

Solve the equation. - $\left( \frac { 1 } { 4 } \right) ^ { x } = 64$

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

Simplify the expression. - eln⁡(0.2)\mathrm { e } ^ { \ln ( 0.2 ) }eln(0.2)

Determine a formula for the exponential function. -

Determine the function which corresponds to the given graph. - The indicated point is (1,−5)( 1 , - 5 )(1,−5) .

Compute the exact value of the function for the given x-value without using a calculator. - f(x)=−7⋅11x for x=1/4f ( x ) = - 7 \cdot 11 ^ { x } \text { for } x = 1 / 4f(x)=−7⋅11x for x=1/4

Assuming all variables are positive, use properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. - log⁡9x\log 9 xlog9x