Question 1

Find the future value.
-$3622 invested for 11 years at 4.6% compounded quarterly

Accepted Answer

A)  $5990.28 
B)  $5973.27 
C)  $6001.80 
D)  $5940.14 
A)  $5990.28 
B)  $5973.27 
C)  $6001.80 
D)  $5940.14

Question 2

Provide an appropriate response.
-Why can' $$y = 2 ^ { x } \text { have an } x \text {-intercept }$$

Accepted Answer

Because no

Question 3

A lake is stocked with 422 fish of a new variety. The size of the lake, the availability of food, and the number of other fish restrict growth in the lake to a limiting value of 2637. The population of fish in the lake after time t, in
Months, is given by the function P(t) $P ( t ) = \frac { 2637 } { 1 + 5.05 e ^ { - 0.39 t } }$ . Find the population after 1 months.

Accepted Answer

A)  597 fish 
B)  612 fish 
C)  587 fish 
D)  607 fish 
A)  597 fish 
B)  612 fish 
C)  587 fish 
D)  607 fish

Question 4

If the function is one-to-one, find its inverse. If not, write "not one-to-one."
-$$f ( x ) = 2 x + 3$$

Accepted Answer

A)  not a one-to-one 
B)  $f ^ { - 1 } ( x ) = \frac { x } { 2 } - 3$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } + 3 } { 2 }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } - 3 } { 2 }$ 
A)  not a one-to-one 
B)  $f ^ { - 1 } ( x ) = \frac { x } { 2 } - 3$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } + 3 } { 2 }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } - 3 } { 2 }$

Question 5

Solve the equation.
-

Accepted Answer

A)  $2 ^ { x + 3 } - 5$ 
B)  $2 ^ { x - 3 } + 5$ 
C)  $2 ^ { x + 3 } + 5$ 
D)  $2 ^ { x - 3 } - 5$ 
A)  $2 ^ { x + 3 } - 5$ 
B)  $2 ^ { x - 3 } + 5$ 
C)  $2 ^ { x + 3 } + 5$ 
D)  $2 ^ { x - 3 } - 5$

Question 6

The population of a particular city is increasing at a rate proportional to its size. It follows the function P(t) = 1 + ke0.12t where k is a constant and t is the time in years. If the current population is 26,000, in how many
Years is the population expected to be 65,000?

Accepted Answer

A)  55 yr 
B)  3 yr 
C)  8 yr 
D)  5 yr 
A)  55 yr 
B)  3 yr 
C)  8 yr 
D)  5 yr

Question 7

Solve the following graphically. If necessary, round answers to the nearest thousandth.
-$$e ^ { x } - 10 = - 21 e ^ { - x }$$

Accepted Answer

A)  $\{ 0.845,0.477 \}$ 
B)  $\{ - 1 \}$ 
C)  $\{ 1.946,1.099 \}$ 
D)  $\{ 7,3 \}$ 
A)  $\{ 0.845,0.477 \}$ 
B)  $\{ - 1 \}$ 
C)  $\{ 1.946,1.099 \}$ 
D)  $\{ 7,3 \}$

Question 8

models salinity of ocean water to depths of 1000 meters at a certain latitude. x is the depth in meters and f(x) is in grams of salt per kilogram of seawater. Approximate the salinity (to the
Nearest hundredth) when the depth is 77 meters.

Accepted Answer

A)  31.67 g/kg 
B)  56.83 g/kg 
C)  -27.13 g/kg 
D)  54.43 g/kg 
A)  31.67 g/kg 
B)  56.83 g/kg 
C)  -27.13 g/kg 
D)  54.43 g/kg

Question 9

How long will it take for $8200 to grow to $42,000 at an interest rate of 4.7% if the interest is compounded continuously? Round the number of years to the nearest hundredth.

Accepted Answer

A)  34.76 yr 
B)  1.11 yr 
C)  3475.61 yr 
D)  3.48 yr 
A)  34.76 yr 
B)  1.11 yr 
C)  3475.61 yr 
D)  3.48 yr

Question 10

At what interest rate must $5000 be compounded annually to equal $7116.56 after 9 yr? (Round to the nearest percent.)

Accepted Answer

A)  3% 
B)  4% 
C)  5% 
D)  6% 
A)  3% 
B)  4% 
C)  5% 
D)  6%

Question 11

Provide an appropriate response.
-Use the properties of exponents to write the function of the form $f ( t ) = k a t$, where $k$ is a constant. $f ( t ) = 3 ^ { 2 t + 3 }$

Accepted Answer

A)  $f ( t ) = 27 \cdot 9 ^ { t }$ 
B)  $f ( t ) = 9 ^ { t } + 27$ 
C)  $f ( t ) = 9 \cdot 27 ^ { t }$ 
D)  $f ( t ) = 27 \cdot 3 ^ { 2 t }$ 
A)  $f ( t ) = 27 \cdot 9 ^ { t }$ 
B)  $f ( t ) = 9 ^ { t } + 27$ 
C)  $f ( t ) = 9 \cdot 27 ^ { t }$ 
D)  $f ( t ) = 27 \cdot 3 ^ { 2 t }$

Question 12

Determine the function value.
-Suppose $f ( x ) = \log _ { a } x$ and $f ( 7 ) = 2$. Find $f ( 49 )$.

Accepted Answer

A)  8 
B)  $- 4$ 
C)  4 
D)  2 
A)  8 
B)  $- 4$ 
C)  4 
D)  2

Question 13

Use a graphing calculator to graph the function using the given viewing window. Use the graph to decide if the function
is one-to-one. If the function is one-to-one, give the equation of the inverse function.
-$$f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - x + 3 ; [ - 2,4 ] \text { by } [ - 20,20 ]$$

Accepted Answer

A)  not one-to-one 
B)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } - 3 } - \mathrm { x }$ 
C)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } ^ { 2 } - 3 \mathrm { x } + 3 }$ 
D)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } - 3 }$ 
A)  not one-to-one 
B)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } - 3 } - \mathrm { x }$ 
C)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } ^ { 2 } - 3 \mathrm { x } + 3 }$ 
D)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } - 3 }$

Question 14

Write the algebraic equation which can be used to find the exact solution of log5 $5 ( x + 5 ) = \frac { - 35 } { x + 7 }$

Accepted Answer

The answer of Write the algebraic equation which can be...

Question 15

Solve the equation.
-$$\left( \frac { 1 } { 2 } \right) ^ { x } = 8$$

Accepted Answer

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

Question 16

NO -Q

Accepted Answer

It appears that there is a misunderstand

Question 17

Solve for the indicated variable.
-$\mathrm { T } = \mathrm { T } _ { 0 } \mathrm { e } ^ { \mathrm { kt } / 300 }$, for $\mathrm { t }$

Accepted Answer

A)  $t = \frac { k } { 300 } \ln \frac { T } { T _ { 0 } }$ 
B)  $t = \frac { 300 } { k } \ln \left( T - T _ { 0 } \right)$ 
C)  $t = \frac { 300 \mathrm {~T} } { \mathrm { kT } _ { 0 } }$ 
D)  $t = \frac { 300 } { k } \ln \frac { T } { T _ { 0 } }$ 
A)  $t = \frac { k } { 300 } \ln \frac { T } { T _ { 0 } }$ 
B)  $t = \frac { 300 } { k } \ln \left( T - T _ { 0 } \right)$ 
C)  $t = \frac { 300 \mathrm {~T} } { \mathrm { kT } _ { 0 } }$ 
D)  $t = \frac { 300 } { k } \ln \frac { T } { T _ { 0 } }$

Question 18

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $a \neq 1 \text { and } b \neq 1$ .
-$$\frac { 1 } { 3 } \log _ { 3 } x ^ { 6 } + \frac { 1 } { 6 } \log _ { 3 } x ^ { 6 } - \frac { 1 } { 9 } \log _ { 3 } x$$

Accepted Answer

A)  $\frac { 7 } { 9 } \log _ { 3 } \left( x ^ { 12 } \right)$ 
B)  $\log _ { 3 } \left( x ^ { 26 / 9 } \right)$ 
C)  $\log _ { 3 } \left( x ^ { 9 / 2 } \right)$ 
D)  $\log _ { 3 } \left( x ^ { 7 } \right)$ 
A)  $\frac { 7 } { 9 } \log _ { 3 } \left( x ^ { 12 } \right)$ 
B)  $\log _ { 3 } \left( x ^ { 26 / 9 } \right)$ 
C)  $\log _ { 3 } \left( x ^ { 9 / 2 } \right)$ 
D)  $\log _ { 3 } \left( x ^ { 7 } \right)$

Question 19

Write an equation for the graph given. The graph represents an logarithmic function f with base 2 or 3, translated and/or
reflected.
-

Accepted Answer

A)  $\log _ { 3 } ( - x - 2 )$ 
B)  $- \log _ { 3 } ( x - 2 )$ 
C)  $- \log _ { 3 } ( \mathrm { x } + 2 )$ 
D)  $- \log _ { 3 } ( - x + 2 )$ 
A)  $\log _ { 3 } ( - x - 2 )$ 
B)  $- \log _ { 3 } ( x - 2 )$ 
C)  $- \log _ { 3 } ( \mathrm { x } + 2 )$ 
D)  $- \log _ { 3 } ( - x + 2 )$

Question 20

An everyday activity is described. Keeping in mind that an inverse operation "undoes" what an operation does, describe each inverse activity.
-waking up

Accepted Answer

A)  going to bed 
B)  closing the eyes 
C)  falling asleep 
D)  getting up 
A)  going to bed 
B)  closing the eyes 
C)  falling asleep 
D)  getting up

Find the future value. -$3622 invested for 11 years at 4.6% compounded quarterly

Provide an appropriate response. -Why can' $y = 2 ^ { x } \text { have an } x \text {-intercept }$

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - $f ( x ) = 2 x + 3$

Solve the equation. -

The population of a particular city is increasing at a rate proportional to its size. It follows the function P(t) = 1 + ke0.12t where k is a constant and t is the time in years. If the current population is 26,000, in how many Years is the population expected to be 65,000?

Solve the following graphically. If necessary, round answers to the nearest thousandth. - $e ^ { x } - 10 = - 21 e ^ { - x }$

models salinity of ocean water to depths of 1000 meters at a certain latitude. x is the depth in meters and f(x) is in grams of salt per kilogram of seawater. Approximate the salinity (to the Nearest hundredth) when the depth is 77 meters.

How long will it take for $8200 to grow to $42,000 at an interest rate of 4.7% if the interest is compounded continuously? Round the number of years to the nearest hundredth.

At what interest rate must $5000 be compounded annually to equal $7116.56 after 9 yr? (Round to the nearest percent.)

Provide an appropriate response. -Use the properties of exponents to write the function of the form $f ( t ) = k a t$ , where $k$ is a constant. $f ( t ) = 3 ^ { 2 t + 3 }$

Determine the function value. -Suppose $f ( x ) = \log _ { a } x$ and $f ( 7 ) = 2$ . Find $f ( 49 )$ .

Use a graphing calculator to graph the function using the given viewing window. Use the graph to decide if the function is one-to-one. If the function is one-to-one, give the equation of the inverse function. - $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - x + 3 ; [ - 2,4 ] \text { by } [ - 20,20 ]$

Write the algebraic equation which can be used to find the exact solution of log5 $5 ( x + 5 ) = \frac { - 35 } { x + 7 }$

Solve the equation. - $\left( \frac { 1 } { 2 } \right) ^ { x } = 8$

NO -Q

Solve for the indicated variable. - $\mathrm { T } = \mathrm { T } _ { 0 } \mathrm { e } ^ { \mathrm { kt } / 300 }$ , for $\mathrm { t }$

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $a \neq 1 \text { and } b \neq 1$ . - $\frac { 1 } { 3 } \log _ { 3 } x ^ { 6 } + \frac { 1 } { 6 } \log _ { 3 } x ^ { 6 } - \frac { 1 } { 9 } \log _ { 3 } x$

Write an equation for the graph given. The graph represents an logarithmic function f with base 2 or 3, translated and/or reflected. -

An everyday activity is described. Keeping in mind that an inverse operation "undoes" what an operation does, describe each inverse activity. -waking up

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 5: Inverse, Exponential, and Logarithmic Functions

Find the future value. -$3622 invested for 11 years at 4.6% compounded quarterly

Provide an appropriate response. -Why can' y=2x have an x-intercept y = 2 ^ { x } \text { have an } x \text {-intercept }y=2x have an x-intercept

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - f(x)=2x+3f ( x ) = 2 x + 3f(x)=2x+3

Solve the equation. -

The population of a particular city is increasing at a rate proportional to its size. It follows the function P(t) = 1 + ke0.12t where k is a constant and t is the time in years. If the current population is 26,000, in how many Years is the population expected to be 65,000?

Solve the following graphically. If necessary, round answers to the nearest thousandth. - ex−10=−21e−xe ^ { x } - 10 = - 21 e ^ { - x }ex−10=−21e−x

models salinity of ocean water to depths of 1000 meters at a certain latitude. x is the depth in meters and f(x) is in grams of salt per kilogram of seawater. Approximate the salinity (to the Nearest hundredth) when the depth is 77 meters.

How long will it take for $8200 to grow to $42,000 at an interest rate of 4.7% if the interest is compounded continuously? Round the number of years to the nearest hundredth.

At what interest rate must $5000 be compounded annually to equal $7116.56 after 9 yr? (Round to the nearest percent.)

Provide an appropriate response. -Use the properties of exponents to write the function of the form f(t)=katf ( t ) = k a tf(t)=kat , where kkk is a constant. f(t)=32t+3f ( t ) = 3 ^ { 2 t + 3 }f(t)=32t+3

Determine the function value. -Suppose f(x)=log⁡axf ( x ) = \log _ { a } xf(x)=loga​x and f(7)=2f ( 7 ) = 2f(7)=2 . Find f(49)f ( 49 )f(49) .

Write the algebraic equation which can be used to find the exact solution of log5 5(x+5)=−35x+75 ( x + 5 ) = \frac { - 35 } { x + 7 }5(x+5)=x+7−35​

Solve the equation. - (12)x=8\left( \frac { 1 } { 2 } \right) ^ { x } = 8(21​)x=8

NO -Q

Solve for the indicated variable. - T=T0ekt/300\mathrm { T } = \mathrm { T } _ { 0 } \mathrm { e } ^ { \mathrm { kt } / 300 }T=T0​ekt/300 , for t\mathrm { t }t

Write an equation for the graph given. The graph represents an logarithmic function f with base 2 or 3, translated and/or reflected. -

An everyday activity is described. Keeping in mind that an inverse operation "undoes" what an operation does, describe each inverse activity. -waking up

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Provide an appropriate response. -Why can' $y = 2 ^ { x } \text { have an } x \text {-intercept }$

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - $f ( x ) = 2 x + 3$

Solve the following graphically. If necessary, round answers to the nearest thousandth. - $e ^ { x } - 10 = - 21 e ^ { - x }$

Provide an appropriate response. -Use the properties of exponents to write the function of the form $f ( t ) = k a t$ , where $k$ is a constant. $f ( t ) = 3 ^ { 2 t + 3 }$

Determine the function value. -Suppose $f ( x ) = \log _ { a } x$ and $f ( 7 ) = 2$ . Find $f ( 49 )$ .

Write the algebraic equation which can be used to find the exact solution of log5 $5 ( x + 5 ) = \frac { - 35 } { x + 7 }$

Solve the equation. - $\left( \frac { 1 } { 2 } \right) ^ { x } = 8$

Solve for the indicated variable. - $\mathrm { T } = \mathrm { T } _ { 0 } \mathrm { e } ^ { \mathrm { kt } / 300 }$ , for $\mathrm { t }$