Question 1

Write the expression using only the indicated logarithms.
-$\log _ { 1 / 4 } ( a - b )$ using natural logarithms

Accepted Answer

A)  $\frac { \ln ( a - b ) } { \ln 4 }$ 
B)  $\frac { 1 } { \ln 4 }$ 
C)  $\frac { \ln 4 } { \ln ( a - b ) }$ 
D)  $- \frac { \ln ( a - b ) } { \ln 4 }$ 
A)  $\frac { \ln ( a - b ) } { \ln 4 }$ 
B)  $\frac { 1 } { \ln 4 }$ 
C)  $\frac { \ln 4 } { \ln ( a - b ) }$ 
D)  $- \frac { \ln ( a - b ) } { \ln 4 }$

Question 2

Evaluate the logarithm.
-$\log _ { 13 } \sqrt { 13 }$

Accepted Answer

A)  $- 2$ 
B)  $\frac { 1 } { 2 }$ 
C)  2 
D)  $- \frac { 1 } { 2 }$ 
A)  $- 2$ 
B)  $\frac { 1 } { 2 }$ 
C)  2 
D)  $- \frac { 1 } { 2 }$

Question 3

Solve the problem.
-Find the annual percentage yield if $2372 is invested at 8.5% compounded continuously.

Accepted Answer

A)  11.09 % 
B)  13.31 % 
C)  8.87 % 
D)  15.53 % 
A)  11.09 % 
B)  13.31 % 
C)  8.87 % 
D)  15.53 %

Question 4

Find the domain of the function.
-$$f ( x ) = \log ( x - 10 )$$

Accepted Answer

A)  $( 0 , \infty )$ 
B)  $( 10 , \infty )$ 
C)  $( - 10 , \infty )$ 
D)  $( 1 , \infty )$ 
A)  $( 0 , \infty )$ 
B)  $( 10 , \infty )$ 
C)  $( - 10 , \infty )$ 
D)  $( 1 , \infty )$

Question 5

Find the logistic function that satisfies the given conditions.
-

Accepted Answer

A)  $f ( x ) = 9 \cdot 1.33 ^ { x }$ 
B)  $f ( x ) = 9 \cdot 1.5 ^ { x }$ 
C)  $\mathrm { f } ( \mathrm { x } ) = 6 \cdot 1.5 ^ { \mathrm { x } }$ 
D)  $f ( x ) = 4 \cdot 0.5 ^ { x }$ 
A)  $f ( x ) = 9 \cdot 1.33 ^ { x }$ 
B)  $f ( x ) = 9 \cdot 1.5 ^ { x }$ 
C)  $\mathrm { f } ( \mathrm { x } ) = 6 \cdot 1.5 ^ { \mathrm { x } }$ 
D)  $f ( x ) = 4 \cdot 0.5 ^ { x }$

Question 6

Solve the problem.
-Find the annual percentage yield if the interest rate is 10.0% and interest is compounded daily (n = 365).

Accepted Answer

A)  10.77% 
B)  11.02% 
C)  10.52% 
D)  10.27% 
A)  10.77% 
B)  11.02% 
C)  10.52% 
D)  10.27%

Question 7

Solve the problem.
-The decay of $984 \mathrm { mg }$ of an isotope is given by $\mathrm { A } ( \mathrm { t } ) = 984 \mathrm { e } ^ { - 0.014 \mathrm { t } }$, where $\mathrm { t }$ is time in years. Find the amount left after 12 years.

Accepted Answer

A)  416 
B)  970 
C)  820 
D)  832 
A)  416 
B)  970 
C)  820 
D)  832

Question 8

Solve the problem.
-A cake is removed from an oven at $325 ^ { \circ } \mathrm { F }$ and cools to $150 ^ { \circ } \mathrm { F }$ after 25 minutes in a room $68 ^ { \circ } \mathrm { F }$. How long will it take the cake to cool to $101 ^ { \circ } \mathrm { F }$ ?

Accepted Answer

A)  $80.82 \mathrm {~min}$ 
B)  $44.9 \mathrm {~min}$ 
C)  $26.94 \mathrm {~min}$ 
D)  $58.37 \mathrm {~min}$ 
A)  $80.82 \mathrm {~min}$ 
B)  $44.9 \mathrm {~min}$ 
C)  $26.94 \mathrm {~min}$ 
D)  $58.37 \mathrm {~min}$

Question 9

Determine the function which corresponds to the given graph.
- 
The indicated point is $( 1,2 )$.

Accepted Answer

A)  $y = \ln ( x + 2 )$ 
B)  $y = \ln ( x - 2 )$ 
C)  $y = \ln x - 2$ 
D)  $y = \ln x + 2$ 
A)  $y = \ln ( x + 2 )$ 
B)  $y = \ln ( x - 2 )$ 
C)  $y = \ln x - 2$ 
D)  $y = \ln x + 2$

Question 10

Find the following using a calculator. Round to four decimal places.
-ln 0

Accepted Answer

A)  undefined 
B)  -0.5231 
C)  -0.4874 
D)  -0.4985 
A)  undefined 
B)  -0.5231 
C)  -0.4874 
D)  -0.4985

Question 11

Solve the problem.
-Find the annual percentage yield if the interest rate is 4.0% and interest is compounded monthly.

Accepted Answer

A)  4.07% 
B)  4.32% 
C)  3.82% 
D)  4.57% 
A)  4.07% 
B)  4.32% 
C)  3.82% 
D)  4.57%

Question 12

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?

Accepted Answer

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

Question 13

Graph the function. Describe its position relative to the graph of the indicated basic function.
-$f(x)=4^{x-3}-3 ; \text { relative to } f(x)=4^{x}$

Accepted Answer

A)  Moved left 3 unit(s);
moved down 3 unit(s)
  
B)  Moved right 3 unit(s);
 moved up 3 unit(s)
  
C)  Moved left 3 unit(s);
moved up 3 unit(s)
  
D)  Moved right 3 unit(s);
moved down 3 unit(s)
  
A)  Moved left 3 unit(s);
moved down 3 unit(s)
  
B)  Moved right 3 unit(s);
 moved up 3 unit(s)
  
C)  Moved left 3 unit(s);
moved up 3 unit(s)
  
D)  Moved right 3 unit(s);
moved down 3 unit(s)

Question 14

Solve the problem.
-At what interest rate must $5100 be compounded annually to equal $8189.49 after 7 yr? (Round to the nearest percent.)

Accepted Answer

A)  6% 
B)  7% 
C)  8% 
D)  9% 
A)  6% 
B)  7% 
C)  8% 
D)  9%

Question 15

Find the exponential function that satisfies the given conditions.
-Initial mass $= 499 \mathrm {~g}$, halving once every 23 hours

Accepted Answer

A)  $m ( t ) = 499 \cdot \left( \frac { 1 } { 2 } \right) ^ { 23 t }$ 
B)  $m ( t ) = 499 \cdot 2 ^ { 23 t }$ 
C)  $m ( t ) = 499 \cdot \left( \frac { 1 } { 2 } \right) ^ { t / 23 }$ 
D)  $m ( t ) = 499 \cdot 2 ^ { t / 23 }$ 
A)  $m ( t ) = 499 \cdot \left( \frac { 1 } { 2 } \right) ^ { 23 t }$ 
B)  $m ( t ) = 499 \cdot 2 ^ { 23 t }$ 
C)  $m ( t ) = 499 \cdot \left( \frac { 1 } { 2 } \right) ^ { t / 23 }$ 
D)  $m ( t ) = 499 \cdot 2 ^ { t / 23 }$

Question 16

State whether the function is an exponential growth function or exponential decay function, and describe its end
behavior using limits.
-$$f ( x ) = 0.3 ^ { x }$$

Accepted Answer

A)  Exponential growth function; $\lim _ { x \rightarrow \infty } f ( x ) = 0 ; \lim _ { x \rightarrow \infty } f ( x ) = \infty$ 
B)  Exponential decay function; $\lim _ { x \rightarrow \infty } f ( x ) = 0 ; \lim _ { x \rightarrow \infty } f ( x ) = \infty$ 
C)  Exponential growth function; $\lim _ { x \rightarrow \infty } f ( x ) = \infty ; \lim _ { x \rightarrow \infty } f ( x ) = 0$ 
D)  Exponential decay function; $\lim _ { x \rightarrow \infty } f ( x ) = \infty ; \lim _ { x \rightarrow \infty } f ( x ) = 0$ 
A)  Exponential growth function; $\lim _ { x \rightarrow \infty } f ( x ) = 0 ; \lim _ { x \rightarrow \infty } f ( x ) = \infty$ 
B)  Exponential decay function; $\lim _ { x \rightarrow \infty } f ( x ) = 0 ; \lim _ { x \rightarrow \infty } f ( x ) = \infty$ 
C)  Exponential growth function; $\lim _ { x \rightarrow \infty } f ( x ) = \infty ; \lim _ { x \rightarrow \infty } f ( x ) = 0$ 
D)  Exponential decay function; $\lim _ { x \rightarrow \infty } f ( x ) = \infty ; \lim _ { x \rightarrow \infty } f ( x ) = 0$

Question 17

Solve the problem.
-Find the future value accumulated in an annuity after investing periodic payments of $20 for 19 years at an annual interest rate of 7%, with payments made and credited 12 times per year.

Accepted Answer

A)  $11,382.01 
B)  $5691.01 
C)  $17,073.02 
D)  $9485.01 
A)  $11,382.01 
B)  $5691.01 
C)  $17,073.02 
D)  $9485.01

Question 18

Decide if the function is an exponential function. If it is, state the initial value and the base.
-$$y = - 8 \cdot 4 ^ { x }$$

Accepted Answer

A)  Exponential Function; base $= 4$; initial value $= - 8$ 
B)  Not an exponential function 
C)  Exponential Function; base $= x$; initial value $= - 8$ 
D)  Exponential Function; base $= - 32$; initial value $= 1$ 
A)  Exponential Function; base $= 4$; initial value $= - 8$ 
B)  Not an exponential function 
C)  Exponential Function; base $= x$; initial value $= - 8$ 
D)  Exponential Function; base $= - 32$; initial value $= 1$

Question 19

Use the change of base rule to find the logarithm to four decimal places.
-$\log _ { 8 } 0.278$

Accepted Answer

A)  $- 0.5560$ 
B)  $28.7770$ 
C)  $- 1.6244$ 
D)  $- 0.6156$ 
A)  $- 0.5560$ 
B)  $28.7770$ 
C)  $- 1.6244$ 
D)  $- 0.6156$

Question 20

Solve the problem.
-The hydrogen potential, $\mathrm { pH }$, of a substance is defined by $\mathrm { pH } = - \log \left[ \mathrm { H } ^ { + } \right]$, where $\left[ \mathrm { H } ^ { + } \right]$is measured in moles per liter. Find the pH of a sample of lake water whose $\left[ \mathrm { H } ^ { + } \right]$is $3.05 \times 10 ^ { - 9 }$ moles per liter. (Round to the nearest tenth.)

Accepted Answer

A)  $10.1$ 
B)  $6.4$ 
C)  $7.3$ 
D)  $8.5$ 
A)  $10.1$ 
B)  $6.4$ 
C)  $7.3$ 
D)  $8.5$

Write the expression using only the indicated logarithms. - $\log _ { 1 / 4 } ( a - b )$ using natural logarithms

Evaluate the logarithm. - $\log _ { 13 } \sqrt { 13 }$

Solve the problem. -Find the annual percentage yield if $2372 is invested at 8.5% compounded continuously.

Find the domain of the function. - $f ( x ) = \log ( x - 10 )$

Find the logistic function that satisfies the given conditions. -

Solve the problem. -Find the annual percentage yield if the interest rate is 10.0% and interest is compounded daily (n = 365).

Solve the problem. -The decay of $984 \mathrm { mg }$ of an isotope is given by $\mathrm { A } ( \mathrm { t } ) = 984 \mathrm { e } ^ { - 0.014 \mathrm { t } }$ , where $\mathrm { t }$ is time in years. Find the amount left after 12 years.

Solve the problem. -A cake is removed from an oven at $325 ^ { \circ } \mathrm { F }$ and cools to $150 ^ { \circ } \mathrm { F }$ after 25 minutes in a room $68 ^ { \circ } \mathrm { F }$ . How long will it take the cake to cool to $101 ^ { \circ } \mathrm { F }$ ?

Determine the function which corresponds to the given graph. - The indicated point is $( 1,2 )$ .

Find the following using a calculator. Round to four decimal places. -ln 0

Solve the problem. -Find the annual percentage yield if the interest rate is 4.0% and interest is compounded monthly.

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?

Solve the problem. -At what interest rate must $5100 be compounded annually to equal $8189.49 after 7 yr? (Round to the nearest percent.)

Find the exponential function that satisfies the given conditions. -Initial mass $= 499 \mathrm {~g}$ , halving once every 23 hours

State whether the function is an exponential growth function or exponential decay function, and describe its end behavior using limits. - $f ( x ) = 0.3 ^ { x }$

Solve the problem. -Find the future value accumulated in an annuity after investing periodic payments of $20 for 19 years at an annual interest rate of 7%, with payments made and credited 12 times per year.

Decide if the function is an exponential function. If it is, state the initial value and the base. - $y = - 8 \cdot 4 ^ { x }$

Use the change of base rule to find the logarithm to four decimal places. - $\log _ { 8 } 0.278$

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

Write the expression using only the indicated logarithms. - log⁡1/4(a−b)\log _ { 1 / 4 } ( a - b )log1/4​(a−b) using natural logarithms

Evaluate the logarithm. - log⁡1313\log _ { 13 } \sqrt { 13 }log13​13​