Exam 14: Exponential and Logarithmic Functions

Use the formula $A = p e ^ { r t }$ to find the total amount of money accumulated at the end of the indicated time period by compounding continuously: $1,000 for 2 years at 2%. The choices are rounded to the nearest cent.

(Multiple Choice)

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Question 61

Express the following as a single logarithm. (Assume that all variables represent positive real numbers.) 2 log b x + 6 log b y $-$ 3 log b z

(Short Answer)

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Question 62

Graph the exponential function. $f ( x ) = 5 ^ { x + 2 }$

(Multiple Choice)

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Question 63

Solve the logarithmic equation. $\ln ( 4 x + 1 ) - \ln ( x + 3 ) = \ln 3$

(Short Answer)

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Question 64

Rueben has a finance plan with the furniture store where the $4,770 he spent accrues finance charges at an annual interest rate of 9.3% compounded monthly for 4 years before he starts to make payments. What will be the balance on the account when he begins making payments?

(Multiple Choice)

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Question 65

Perform the following calculations and express answer to the nearest hundredth. $\frac { 5 \ln 8 } { \ln 6 }$

(Multiple Choice)

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Question 66

Express the following as a single logarithm. (Assume that all variables represent positive real numbers.) $3 \log b x + \frac { 1 } { 2 } \log _ { b } ( x - 2 ) - 7 \log b ( 3 x + 8 )$

(Multiple Choice)

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Question 67

Perform the following calculations and express answer to the nearest hundredth. $\frac { \ln 3 } { 0.07 }$

(Multiple Choice)

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Question 68

Solve the exponential equation and express approximate solutions to the nearest hundredth. 8 ^x = 14

(Short Answer)

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Question 69

Graph $y = \log _ { \frac { 1 } { 4 } } x$ by graphing $\left( \frac { 1 } { 4 } \right) ^ { y } = x$ .

(Multiple Choice)

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Question 70

If $k > 0$ , then the formula $Q ( t ) = Q _ { 0 } e ^ { k t }$ is the law of decay model.

(True/False)

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Question 71

True or false? The graph below represents a one-to-one function.

(True/False)

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Question 72

Write $2 ^ { - 3 } = \frac { 1 } { 8 }$ in logarithmic form.

(Short Answer)

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Question 73

Solve the equation. $\log _ { x } 5 = \frac { 1 } { 5 }$

(Short Answer)

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Question 74

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

(Short Answer)

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Question 75

Use a calculator to find each common logarithm. Express answer to four decimal places. $\log x = 4.1655$

(Multiple Choice)

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Question 76

Graph the exponential function. $f ( x ) = 5 ^ { - x - 2 }$

(Multiple Choice)

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Question 77

Use the formula $A = p \left( 1 + \frac { r } { n } \right) ^ { n t }$ to find the amount for the investment. $2,600 for 6 years at 3% compounded quarterly.

(Multiple Choice)

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Question 78

Solve the exponential equation and express approximate solutions to the nearest hundredth. e^{x - 6} = 33

(Multiple Choice)

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Question 79

Write the logarithmic statement in exponential form. $\log 2 \left( \frac { 1 } { 16 } \right) = - 4$

(Multiple Choice)

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Question 80

Use the formula $A = p e ^ { r t }$ to find the total amount of money accumulated at the end of the indicated time period by compounding continuously: $1,000 for 2 years at 2%. The choices are rounded to the nearest cent.

Express the following as a single logarithm. (Assume that all variables represent positive real numbers.) 2 log b x + 6 log b y $-$ 3 log b z

Graph the exponential function. $f ( x ) = 5 ^ { x + 2 }$

Solve the logarithmic equation. $\ln ( 4 x + 1 ) - \ln ( x + 3 ) = \ln 3$

Rueben has a finance plan with the furniture store where the $4,770 he spent accrues finance charges at an annual interest rate of 9.3% compounded monthly for 4 years before he starts to make payments. What will be the balance on the account when he begins making payments?

Perform the following calculations and express answer to the nearest hundredth. $\frac { 5 \ln 8 } { \ln 6 }$

Express the following as a single logarithm. (Assume that all variables represent positive real numbers.) $3 \log b x + \frac { 1 } { 2 } \log _ { b } ( x - 2 ) - 7 \log b ( 3 x + 8 )$

Perform the following calculations and express answer to the nearest hundredth. $\frac { \ln 3 } { 0.07 }$

Solve the exponential equation and express approximate solutions to the nearest hundredth. 8 ^x = 14

Graph $y = \log _ { \frac { 1 } { 4 } } x$ by graphing $\left( \frac { 1 } { 4 } \right) ^ { y } = x$ .

If $k > 0$ , then the formula $Q ( t ) = Q _ { 0 } e ^ { k t }$ is the law of decay model.

True or false? The graph below represents a one-to-one function.

Write $2 ^ { - 3 } = \frac { 1 } { 8 }$ in logarithmic form.

Solve the equation. $\log _ { x } 5 = \frac { 1 } { 5 }$

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

Use a calculator to find each common logarithm. Express answer to four decimal places. $\log x = 4.1655$

Graph the exponential function. $f ( x ) = 5 ^ { - x - 2 }$

Use the formula $A = p \left( 1 + \frac { r } { n } \right) ^ { n t }$ to find the amount for the investment. $2,600 for 6 years at 3% compounded quarterly.

Solve the exponential equation and express approximate solutions to the nearest hundredth. e^{x - 6} = 33

Write the logarithmic statement in exponential form. $\log 2 \left( \frac { 1 } { 16 } \right) = - 4$

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Systems of Equations: Matrices and Determinants

Filters

Exam 14: Exponential and Logarithmic Functions

Use the formula A=pertA = p e ^ { r t }A=pert to find the total amount of money accumulated at the end of the indicated time period by compounding continuously: $1,000 for 2 years at 2%. The choices are rounded to the nearest cent.

Express the following as a single logarithm. (Assume that all variables represent positive real numbers.) 2 log b x + 6 log b y −-− 3 log b z

Graph the exponential function. f(x)=5x+2f ( x ) = 5 ^ { x + 2 }f(x)=5x+2

Solve the logarithmic equation. ln⁡(4x+1)−ln⁡(x+3)=ln⁡3\ln ( 4 x + 1 ) - \ln ( x + 3 ) = \ln 3ln(4x+1)−ln(x+3)=ln3

Rueben has a finance plan with the furniture store where the $4,770 he spent accrues finance charges at an annual interest rate of 9.3% compounded monthly for 4 years before he starts to make payments. What will be the balance on the account when he begins making payments?

Perform the following calculations and express answer to the nearest hundredth. 5ln⁡8ln⁡6\frac { 5 \ln 8 } { \ln 6 }ln65ln8​

Express the following as a single logarithm. (Assume that all variables represent positive real numbers.) 3log⁡bx+12log⁡b(x−2)−7log⁡b(3x+8)3 \log b x + \frac { 1 } { 2 } \log _ { b } ( x - 2 ) - 7 \log b ( 3 x + 8 )3logbx+21​logb​(x−2)−7logb(3x+8)

Perform the following calculations and express answer to the nearest hundredth. ln⁡30.07\frac { \ln 3 } { 0.07 }0.07ln3​

Solve the exponential equation and express approximate solutions to the nearest hundredth. 8 x = 14

Graph y=log⁡14xy = \log _ { \frac { 1 } { 4 } } xy=log41​​x by graphing (14)y=x\left( \frac { 1 } { 4 } \right) ^ { y } = x(41​)y=x .

If k>0k > 0k>0 , then the formula Q(t)=Q0ektQ ( t ) = Q _ { 0 } e ^ { k t }Q(t)=Q0​ekt is the law of decay model.

True or false? The graph below represents a one-to-one function.

Write 2−3=182 ^ { - 3 } = \frac { 1 } { 8 }2−3=81​ in logarithmic form.

Solve the equation. log⁡x5=15\log _ { x } 5 = \frac { 1 } { 5 }logx​5=51​

Solve the equation. 2−x=182 ^ { - x } = \frac { 1 } { 8 }2−x=81​

Use a calculator to find each common logarithm. Express answer to four decimal places. log⁡x=4.1655\log x = 4.1655logx=4.1655

Graph the exponential function. f(x)=5−x−2f ( x ) = 5 ^ { - x - 2 }f(x)=5−x−2

Use the formula A=p(1+rn)ntA = p \left( 1 + \frac { r } { n } \right) ^ { n t }A=p(1+nr​)nt to find the amount for the investment. $2,600 for 6 years at 3% compounded quarterly.

Solve the exponential equation and express approximate solutions to the nearest hundredth. e x - 6 = 33

Write the logarithmic statement in exponential form. log⁡2(116)=−4\log 2 \left( \frac { 1 } { 16 } \right) = - 4log2(161​)=−4

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Systems of Equations: Matrices and Determinants

Filters

Use the formula $A = p e ^ { r t }$ to find the total amount of money accumulated at the end of the indicated time period by compounding continuously: $1,000 for 2 years at 2%. The choices are rounded to the nearest cent.

Express the following as a single logarithm. (Assume that all variables represent positive real numbers.) 2 log b x + 6 log b y $-$ 3 log b z

Graph the exponential function. $f ( x ) = 5 ^ { x + 2 }$

Solve the logarithmic equation. $\ln ( 4 x + 1 ) - \ln ( x + 3 ) = \ln 3$

Perform the following calculations and express answer to the nearest hundredth. $\frac { 5 \ln 8 } { \ln 6 }$

Express the following as a single logarithm. (Assume that all variables represent positive real numbers.) $3 \log b x + \frac { 1 } { 2 } \log _ { b } ( x - 2 ) - 7 \log b ( 3 x + 8 )$

Perform the following calculations and express answer to the nearest hundredth. $\frac { \ln 3 } { 0.07 }$

Solve the exponential equation and express approximate solutions to the nearest hundredth. 8 ^x = 14

Graph $y = \log _ { \frac { 1 } { 4 } } x$ by graphing $\left( \frac { 1 } { 4 } \right) ^ { y } = x$ .

If $k > 0$ , then the formula $Q ( t ) = Q _ { 0 } e ^ { k t }$ is the law of decay model.

Write $2 ^ { - 3 } = \frac { 1 } { 8 }$ in logarithmic form.

Solve the equation. $\log _ { x } 5 = \frac { 1 } { 5 }$

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

Use a calculator to find each common logarithm. Express answer to four decimal places. $\log x = 4.1655$

Graph the exponential function. $f ( x ) = 5 ^ { - x - 2 }$

Use the formula $A = p \left( 1 + \frac { r } { n } \right) ^ { n t }$ to find the amount for the investment. $2,600 for 6 years at 3% compounded quarterly.

Solve the exponential equation and express approximate solutions to the nearest hundredth. e^{x - 6} = 33

Write the logarithmic statement in exponential form. $\log 2 \left( \frac { 1 } { 16 } \right) = - 4$