Question 1

Determine the correct exponential function of the form f(x) = bS1U1P1xS1S1P0 whose graph is given.
-

Accepted Answer

A)  $f ( x ) = 5 ^ { x }$ 
B)  $f ( x ) = \left( \frac { 1 } { 25 } \right) ^ { x }$ 
C)  $f ( x ) = 25 ^ { x }$ 
D)  $f ( x ) = \left( \frac { 1 } { 5 } \right) ^ { x }$ 
A)  $f ( x ) = 5 ^ { x }$ 
B)  $f ( x ) = \left( \frac { 1 } { 25 } \right) ^ { x }$ 
C)  $f ( x ) = 25 ^ { x }$ 
D)  $f ( x ) = \left( \frac { 1 } { 5 } \right) ^ { x }$

Question 2

Solve the problem.
-A bacterial culture has an initial population of 10,000. If its population declines to 6000 in 8 hours, what will it be at the end of 10 hours? Assume that the population decreases according to the exponential model.

Accepted Answer

A) 2000 
B) 5281 
C) 5061 
D) 2641 
A) 2000 
B) 5281 
C) 5061 
D) 2641

Question 3

Evaluate the expression without the use of a calculator, and then verify your answer using a calculator.
-$\mathrm { e } ^ { \ln 8 }$

Accepted Answer

A)  7 
B)  $e ^ { 8 }$ 
C)  8 
D)  $\ln 8$ 
A)  7 
B)  $e ^ { 8 }$ 
C)  8 
D)  $\ln 8$

Question 4

Solve the equation.
-$\log _ { 8 } ( 4 x + 2 ) = \log _ { 8 } ( 4 x + 5 )$

Accepted Answer

A)  $\{ 3 \}$ 
B)  $\{ 0 \}$ 
C)  $\left\{ \frac { 7 } { 3 } \right\}$ 
D)  $\varnothing$ 
A)  $\{ 3 \}$ 
B)  $\{ 0 \}$ 
C)  $\left\{ \frac { 7 } { 3 } \right\}$ 
D)  $\varnothing$

Question 5

Find the domain of the function.
-$$f ( x ) = \log \left( \frac { x + 2 } { x - 8 } \right)$$

Accepted Answer

A)  $( - \infty , - 2 )$ 
B)  $( 8 , \infty )$ 
C)  $( - \infty , - 2 ) \cup ( 8 , \infty )$ 
D)  $( - 2,8 )$ 
A)  $( - \infty , - 2 )$ 
B)  $( 8 , \infty )$ 
C)  $( - \infty , - 2 ) \cup ( 8 , \infty )$ 
D)  $( - 2,8 )$

Question 6

Graph the function.
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Accepted Answer

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

Determine the correct exponential function of the form f(x) = b^x whose graph is given. -

Solve the problem. -A bacterial culture has an initial population of 10,000. If its population declines to 6000 in 8 hours, what will it be at the end of 10 hours? Assume that the population decreases according to the exponential model.

Evaluate the expression without the use of a calculator, and then verify your answer using a calculator. - $\mathrm { e } ^ { \ln 8 }$

Solve the equation. - $\log _ { 8 } ( 4 x + 2 ) = \log _ { 8 } ( 4 x + 5 )$

Find the domain of the function. - $f ( x ) = \log \left( \frac { x + 2 } { x - 8 } \right)$

Graph the function. -

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Exam 5: Exponential and Logarithmic Functions and Equations

Determine the correct exponential function of the form f(x) = bx whose graph is given. -