Fill in the blank with one of the words or phrases listed below. Some words or phrases may be used more than once. \[\begin{array} { l l l l } \text { inverse } & \text { common } & \text { composition symmetric } & \text { exponential } \\ \text { vertical } & \text { logarithmic } & \text { natural } \quad \text { half-life } & \text { horizontal } \end{array}\] ------------is the amount of time it takes for half of the amount of a substance to decay.

A) Exponential B) Half-life C) Composition D) Logarithmic A) Exponential B) Half-life C) Composition D) Logarithmic

Fill in the blank with one of the words or phrases listed below. Some words or phrases may be used more than once. \[\begin{array} { l l l l } \text { inverse } & \text { common } & \text { composition symmetric } & \text { exponential } \\ \text { vertical } & \text { logarithmic } & \text { natural } \quad \text { half-life } & \text { horizontal } \end{array}\] -A(n) ----------function is a function that can be defined by f(x) = logbx, where x is a positive real number, b is a constant positive real number, and b is not 1.

A) logarithmic B) symmetric C) exponential D) inverse A) logarithmic B) symmetric C) exponential D) inverse

Write the function F(x) as a composition of f, g, or h. -$\begin{array} { l } f ( x ) = x ^ { 2 } + 8 \quad g ( x ) = 2 x \quad h ( x ) = \sqrt { x + 5 } \\ F ( x ) = x + 13 \end{array}$

A) $F ( x ) = ( h \circ g ) ( x )$ B) $F ( x ) = ( f \circ h ) ( x )$ C) $F ( x ) = ( f \circ g ) ( x )$ D) $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { g } \circ \mathrm { h } ) ( \mathrm { x } )$ A) $F ( x ) = ( h \circ g ) ( x )$ B) $F ( x ) = ( f \circ h ) ( x )$ C) $F ( x ) = ( f \circ g ) ( x )$ D) $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { g } \circ \mathrm { h } ) ( \mathrm { x } )$

Exam 12: Exponential and Logarithmic Functions

Use the formula A $A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { to solve. }$ -Suppose that you have $7000 to invest. Which investment yields the greater return over 6 years: 6.6% compounded monthly or 6.7% compounded quarterly?

(Multiple Choice)

4.9/5

(33)

Question 201

Determine whether the graph of the function is the graph of a one-to-one function. -

(True/False)

4.8/5

(34)

Question 202

Fill in the blank with one of the words or phrases listed below. Some words or phrases may be used more than once. inverse common composition symmetric exponential vertical logarithmic natural half-life horizontal ------------is the amount of time it takes for half of the amount of a substance to decay.

(Multiple Choice)

4.9/5

(31)

Question 203

Use the exponential decay formula to find the final amount. Round to the nearest whole. -

(Multiple Choice)

4.8/5

(38)

Question 204

Solve the equation. - $4 ^ { ( 3 x - 7 ) } = 16$

(Multiple Choice)

4.8/5

(29)

Question 205

Use the exponential decay formula to find the final amount. Round to the nearest whole. -

(Multiple Choice)

4.8/5

(32)

Question 206

Use the exponential decay formula with half-lives to find the final amount. Round to the nearest tenth when necessary. -

(Multiple Choice)

4.8/5

(45)

Question 207

Fill in the blank with one of the words or phrases listed below. Some words or phrases may be used more than once. inverse common composition symmetric exponential vertical logarithmic natural half-life horizontal -A(n) ----------function is a function that can be defined by f(x) = logbx, where x is a positive real number, b is a constant positive real number, and b is not 1.

(Multiple Choice)

4.9/5

(43)

Question 208

Simplify. - $\log _ { 3 } 1$

(Multiple Choice)

4.8/5

(39)

Question 209

Solve the equation. - $\log _ { 3 } 5 - \log _ { 3 } x = 3$

(Multiple Choice)

4.9/5

(31)

Question 210

For the given functions f and g, find the requested function. - $f ( x ) = - 6 x ^ { 4 } ; g ( x ) = - 2 x ^ { 2 } \quad$ Find $\left( \frac { f } { g } \right) ( x )$ .

(Multiple Choice)

4.9/5

(29)

Question 211

Solve. -Four bacteria are placed in a petri dish. The population will triple every day. The formula for the number of bacteria in the dish on day $t$ is $N ( t ) = 4 ( 3 ) ^ { t }$ , where $t$ is the number of days after the four bacteria are placed in the dish. How many bacteria are in the dish seven days after the four bacteria are placed in the dish?

(Multiple Choice)

4.8/5

(39)

Question 212

Simplify. - $\log _ { 5 } 5$

(Multiple Choice)

4.9/5

(47)

Question 213

Write the function F(x) as a composition of f, g, or h. - f(x)=+8g(x)=2xh(x)= F(x)=x+13

(Multiple Choice)

5.0/5

(47)

Question 214

Determine whether the function is a one-to-one function. - $f = \{ ( - 3,2 ) , ( - 2,3 ) , ( - 5 , - 3 ) , ( 5,3 ) \}$

(Multiple Choice)

4.8/5

(32)

Question 215

Solve. -Find out how long it takes a $\$ 2900$ investment to earn $\$ 400$ interest if it is invested at $7 \%$ compounded semiannually. Round to the nearest tenth of a year. Use the formula $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$ .

(Multiple Choice)

4.7/5

(44)

Question 216

Given the values of f and g, find the function value. - $f ( 9 ) = 20 ; g ( 9 ) = 5 \quad$ Find $\left( \frac { f } { g } \right) ( 9 )$

(Multiple Choice)

4.9/5

(30)

Question 217

Solve the equation. - $\log 7.06 + 3 \log x - \log x ^ { 2 } = \log 7.06 + 6$

(Multiple Choice)

4.7/5

(40)

Question 218

Find the value of the logarithmic expression. - $\log _ { 1 / 8 } 8$

(Multiple Choice)

4.9/5

(28)

Question 219

Solve the equation for x. Give an approximate solution accurate to four decimal places. - $\log 17 x = 1.1$

(Multiple Choice)

4.8/5

(23)

Question 220

Use the formula A $A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { to solve. }$ -Suppose that you have $7000 to invest. Which investment yields the greater return over 6 years: 6.6% compounded monthly or 6.7% compounded quarterly?

Determine whether the graph of the function is the graph of a one-to-one function. -

Use the exponential decay formula to find the final amount. Round to the nearest whole. -

Solve the equation. - $4 ^ { ( 3 x - 7 ) } = 16$

Use the exponential decay formula to find the final amount. Round to the nearest whole. -

Use the exponential decay formula with half-lives to find the final amount. Round to the nearest tenth when necessary. -

Simplify. - $\log _ { 3 } 1$

Solve the equation. - $\log _ { 3 } 5 - \log _ { 3 } x = 3$

For the given functions f and g, find the requested function. - $f ( x ) = - 6 x ^ { 4 } ; g ( x ) = - 2 x ^ { 2 } \quad$ Find $\left( \frac { f } { g } \right) ( x )$ .

Simplify. - $\log _ { 5 } 5$

Write the function F(x) as a composition of f, g, or h. - f(x)=+8g(x)=2xh(x)= F(x)=x+13

Determine whether the function is a one-to-one function. - $f = \{ ( - 3,2 ) , ( - 2,3 ) , ( - 5 , - 3 ) , ( 5,3 ) \}$

Solve. -Find out how long it takes a $\$ 2900$ investment to earn $\$ 400$ interest if it is invested at $7 \%$ compounded semiannually. Round to the nearest tenth of a year. Use the formula $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$ .

Given the values of f and g, find the function value. - $f ( 9 ) = 20 ; g ( 9 ) = 5 \quad$ Find $\left( \frac { f } { g } \right) ( 9 )$

Solve the equation. - $\log 7.06 + 3 \log x - \log x ^ { 2 } = \log 7.06 + 6$

Find the value of the logarithmic expression. - $\log _ { 1 / 8 } 8$

Solve the equation for x. Give an approximate solution accurate to four decimal places. - $\log 17 x = 1.1$

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 12: Exponential and Logarithmic Functions

Use the formula A A=P(1+rn)nt to solve. A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { to solve. }A=P(1+nr​)nt to solve. -Suppose that you have $7000 to invest. Which investment yields the greater return over 6 years: 6.6% compounded monthly or 6.7% compounded quarterly?

Determine whether the graph of the function is the graph of a one-to-one function. -

Use the exponential decay formula to find the final amount. Round to the nearest whole. -

Solve the equation. - 4(3x−7)=164 ^ { ( 3 x - 7 ) } = 164(3x−7)=16

Use the exponential decay formula to find the final amount. Round to the nearest whole. -

Use the exponential decay formula with half-lives to find the final amount. Round to the nearest tenth when necessary. -

Simplify. - log⁡31\log _ { 3 } 1log3​1

Solve the equation. - log⁡35−log⁡3x=3\log _ { 3 } 5 - \log _ { 3 } x = 3log3​5−log3​x=3

For the given functions f and g, find the requested function. - f(x)=−6x4;g(x)=−2x2f ( x ) = - 6 x ^ { 4 } ; g ( x ) = - 2 x ^ { 2 } \quadf(x)=−6x4;g(x)=−2x2 Find (fg)(x)\left( \frac { f } { g } \right) ( x )(gf​)(x) .

Simplify. - log⁡55\log _ { 5 } 5log5​5

Write the function F(x) as a composition of f, g, or h. - f(x)=+8g(x)=2xh(x)= F(x)=x+13

Determine whether the function is a one-to-one function. - f={(−3,2),(−2,3),(−5,−3),(5,3)}f = \{ ( - 3,2 ) , ( - 2,3 ) , ( - 5 , - 3 ) , ( 5,3 ) \}f={(−3,2),(−2,3),(−5,−3),(5,3)}

Solve. -Find out how long it takes a $2900\$ 2900$2900 investment to earn $400\$ 400$400 interest if it is invested at 7%7 \%7% compounded semiannually. Round to the nearest tenth of a year. Use the formula A=P(1+rn)ntA = P \left( 1 + \frac { r } { n } \right) ^ { n t }A=P(1+nr​)nt .

Given the values of f and g, find the function value. - f(9)=20;g(9)=5f ( 9 ) = 20 ; g ( 9 ) = 5 \quadf(9)=20;g(9)=5 Find (fg)(9)\left( \frac { f } { g } \right) ( 9 )(gf​)(9)

Solve the equation. - log⁡7.06+3log⁡x−log⁡x2=log⁡7.06+6\log 7.06 + 3 \log x - \log x ^ { 2 } = \log 7.06 + 6log7.06+3logx−logx2=log7.06+6

Find the value of the logarithmic expression. - log⁡1/88\log _ { 1 / 8 } 8log1/8​8

Solve the equation for x. Give an approximate solution accurate to four decimal places. - log⁡17x=1.1\log 17 x = 1.1log17x=1.1

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Use the formula A $A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { to solve. }$ -Suppose that you have $7000 to invest. Which investment yields the greater return over 6 years: 6.6% compounded monthly or 6.7% compounded quarterly?

Solve the equation. - $4 ^ { ( 3 x - 7 ) } = 16$

Simplify. - $\log _ { 3 } 1$

Solve the equation. - $\log _ { 3 } 5 - \log _ { 3 } x = 3$

For the given functions f and g, find the requested function. - $f ( x ) = - 6 x ^ { 4 } ; g ( x ) = - 2 x ^ { 2 } \quad$ Find $\left( \frac { f } { g } \right) ( x )$ .

Simplify. - $\log _ { 5 } 5$

Determine whether the function is a one-to-one function. - $f = \{ ( - 3,2 ) , ( - 2,3 ) , ( - 5 , - 3 ) , ( 5,3 ) \}$

Solve. -Find out how long it takes a $\$ 2900$ investment to earn $\$ 400$ interest if it is invested at $7 \%$ compounded semiannually. Round to the nearest tenth of a year. Use the formula $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$ .

Given the values of f and g, find the function value. - $f ( 9 ) = 20 ; g ( 9 ) = 5 \quad$ Find $\left( \frac { f } { g } \right) ( 9 )$

Solve the equation. - $\log 7.06 + 3 \log x - \log x ^ { 2 } = \log 7.06 + 6$

Find the value of the logarithmic expression. - $\log _ { 1 / 8 } 8$

Solve the equation for x. Give an approximate solution accurate to four decimal places. - $\log 17 x = 1.1$