Exam 9: Exponential and Logarithmic Functions

An initial deposit of $30,000 earns 12% interest, compounded monthly. How much will be in the account after 10 years? Please give the answer to two decimal places.

(Short Answer)

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Question 81

Solve for x . $\log _ { 2 } x = 5$

(Short Answer)

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Question 82

If $f ( x ) = x ^ { 3 } \text { and } g ( x ) =$ __________, then $( f \circ g ) ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 27 x + 27$

(Short Answer)

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Question 83

Determine whether the function is one-to-one. $f ( x ) = x ^ { 3 } + 6$ Answer yes or no .

(Short Answer)

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Question 84

Solve the equation. Give the exact answer in terms of ln . $e ^ { 2 t } = 7$

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Question 85

Assume that $\log _ { 5 } 9$ , $\log _ { b } 7 = 0.8451$ and $\log _ { b } 9 = 0.9542$ . Use these values to evaluate the logarithm. $\log _ { b } 63$

(Short Answer)

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Question 86

Evaluate the expression. $\log _ { 5 } 9$

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Question 87

The logarithm of a number to a power equals the _________ times the logarithm of the number.

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Question 88

Evaluate the expression. $\log _ { 5 } 9$

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Question 89

Solve the equation. ${ } ^ { 227 } \mathrm { Th }$

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Question 90

An initial deposit of $30,000 earns 4% interest, compounded quarterly. How much will be in the account after 10 years? Please give the answer to two decimal places.

(Short Answer)

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Question 91

Graph $f ( x ) = 2 ^ { x } - 2$ by plotting points or using a translation. $Graph f ( x ) = 2 ^ { x } - 2 by plotting points or using a translation.$

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Question 92

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify, if possible. Assume that q and w are positive numbers. $\log _ { 2 } \frac { q w } { 4 }$

(Essay)

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Question 93

Find the inverse of the function and express it using $f ^ { - 1 } ( x )$ notation. $f ( x ) = 4 x - 1$

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Question 94

If j gets larger and larger, the value of $\left( 1 + \frac { 1 } { j } \right) ^ { j }$ approaches the value of __________.

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Question 95

To save for college, parents invest $20,000 for their newborn child in a mutual fund that should average 12% annual return. If the semiannually dividends are reinvested, how much will be available in 19 years? Round your answer to the nearest cent.

(Short Answer)

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Question 96

Evaluate the expression. $\log _ { 3 } 81$

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Question 97

The half-life of tritium is 12.4 years. How long will it take for 25% of a sample of tritium to decompose? Please round the answer to the nearest tenth. __________ years

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Question 98

Solve the equation. ${ } ^ { 227 } \mathrm { Th }$

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Question 99

What is the name of the function $f ( x ) = e ^ { x }$ ? $What is the name of the function f ( x ) = e ^ { x } ?$

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Question 100

An initial deposit of $30,000 earns 12% interest, compounded monthly. How much will be in the account after 10 years? Please give the answer to two decimal places.

Solve for x . $\log _ { 2 } x = 5$

If $f ( x ) = x ^ { 3 } \text { and } g ( x ) =$ __________, then $( f \circ g ) ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 27 x + 27$

Determine whether the function is one-to-one. $f ( x ) = x ^ { 3 } + 6$ Answer yes or no .

Solve the equation. Give the exact answer in terms of ln . $e ^ { 2 t } = 7$

Assume that $\log _ { 5 } 9$ , $\log _ { b } 7 = 0.8451$ and $\log _ { b } 9 = 0.9542$ . Use these values to evaluate the logarithm. $\log _ { b } 63$

Evaluate the expression. $\log _ { 5 } 9$

The logarithm of a number to a power equals the _________ times the logarithm of the number.

Evaluate the expression. $\log _ { 5 } 9$

Solve the equation. ${ } ^ { 227 } \mathrm { Th }$

An initial deposit of $30,000 earns 4% interest, compounded quarterly. How much will be in the account after 10 years? Please give the answer to two decimal places.

Graph $f ( x ) = 2 ^ { x } - 2$ by plotting points or using a translation. $Graph f ( x ) = 2 ^ { x } - 2 by plotting points or using a translation.$

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify, if possible. Assume that q and w are positive numbers. $\log _ { 2 } \frac { q w } { 4 }$

Find the inverse of the function and express it using $f ^ { - 1 } ( x )$ notation. $f ( x ) = 4 x - 1$

If j gets larger and larger, the value of $\left( 1 + \frac { 1 } { j } \right) ^ { j }$ approaches the value of __________.

To save for college, parents invest $20,000 for their newborn child in a mutual fund that should average 12% annual return. If the semiannually dividends are reinvested, how much will be available in 19 years? Round your answer to the nearest cent.

Evaluate the expression. $\log _ { 3 } 81$

The half-life of tritium is 12.4 years. How long will it take for 25% of a sample of tritium to decompose? Please round the answer to the nearest tenth. __________ years

Solve the equation. ${ } ^ { 227 } \mathrm { Th }$

What is the name of the function $f ( x ) = e ^ { x }$ ? $What is the name of the function f ( x ) = e ^ { x } ?$

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Rational Expression and Equations

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Exam 9: Exponential and Logarithmic Functions

An initial deposit of $30,000 earns 12% interest, compounded monthly. How much will be in the account after 10 years? Please give the answer to two decimal places.

Solve for x . log⁡2x=5\log _ { 2 } x = 5log2​x=5

If f(x)=x3 and g(x)=f ( x ) = x ^ { 3 } \text { and } g ( x ) =f(x)=x3 and g(x)= __________, then (f∘g)(x)=x3+9x2+27x+27( f \circ g ) ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 27 x + 27(f∘g)(x)=x3+9x2+27x+27

Determine whether the function is one-to-one. f(x)=x3+6f ( x ) = x ^ { 3 } + 6f(x)=x3+6 Answer yes or no .

Solve the equation. Give the exact answer in terms of ln . e2t=7e ^ { 2 t } = 7e2t=7

Assume that log⁡59\log _ { 5 } 9log5​9 , log⁡b7=0.8451\log _ { b } 7 = 0.8451logb​7=0.8451 and log⁡b9=0.9542\log _ { b } 9 = 0.9542logb​9=0.9542 . Use these values to evaluate the logarithm. log⁡b63\log _ { b } 63logb​63

Evaluate the expression. log⁡59\log _ { 5 } 9log5​9

The logarithm of a number to a power equals the _________ times the logarithm of the number.

Evaluate the expression. log⁡59\log _ { 5 } 9log5​9

Solve the equation. 227Th{ } ^ { 227 } \mathrm { Th }227Th

An initial deposit of $30,000 earns 4% interest, compounded quarterly. How much will be in the account after 10 years? Please give the answer to two decimal places.

Graph f(x)=2x−2f ( x ) = 2 ^ { x } - 2f(x)=2x−2 by plotting points or using a translation.

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify, if possible. Assume that q and w are positive numbers. log⁡2qw4\log _ { 2 } \frac { q w } { 4 }log2​4qw​

Find the inverse of the function and express it using f−1(x)f ^ { - 1 } ( x )f−1(x) notation. f(x)=4x−1f ( x ) = 4 x - 1f(x)=4x−1

If j gets larger and larger, the value of (1+1j)j\left( 1 + \frac { 1 } { j } \right) ^ { j }(1+j1​)j approaches the value of __________.

To save for college, parents invest $20,000 for their newborn child in a mutual fund that should average 12% annual return. If the semiannually dividends are reinvested, how much will be available in 19 years? Round your answer to the nearest cent.

Evaluate the expression. log⁡381\log _ { 3 } 81log3​81

The half-life of tritium is 12.4 years. How long will it take for 25% of a sample of tritium to decompose? Please round the answer to the nearest tenth. __________ years

Solve the equation. 227Th{ } ^ { 227 } \mathrm { Th }227Th

What is the name of the function f(x)=exf ( x ) = e ^ { x }f(x)=ex ?

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Rational Expression and Equations

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Solve for x . $\log _ { 2 } x = 5$

If $f ( x ) = x ^ { 3 } \text { and } g ( x ) =$ __________, then $( f \circ g ) ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 27 x + 27$

Determine whether the function is one-to-one. $f ( x ) = x ^ { 3 } + 6$ Answer yes or no .

Solve the equation. Give the exact answer in terms of ln . $e ^ { 2 t } = 7$

Assume that $\log _ { 5 } 9$ , $\log _ { b } 7 = 0.8451$ and $\log _ { b } 9 = 0.9542$ . Use these values to evaluate the logarithm. $\log _ { b } 63$

Evaluate the expression. $\log _ { 5 } 9$

Evaluate the expression. $\log _ { 5 } 9$

Solve the equation. ${ } ^ { 227 } \mathrm { Th }$

Graph $f ( x ) = 2 ^ { x } - 2$ by plotting points or using a translation. $Graph f ( x ) = 2 ^ { x } - 2 by plotting points or using a translation.$

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify, if possible. Assume that q and w are positive numbers. $\log _ { 2 } \frac { q w } { 4 }$

Find the inverse of the function and express it using $f ^ { - 1 } ( x )$ notation. $f ( x ) = 4 x - 1$

If j gets larger and larger, the value of $\left( 1 + \frac { 1 } { j } \right) ^ { j }$ approaches the value of __________.

Evaluate the expression. $\log _ { 3 } 81$

Solve the equation. ${ } ^ { 227 } \mathrm { Th }$

What is the name of the function $f ( x ) = e ^ { x }$ ? $What is the name of the function f ( x ) = e ^ { x } ?$