Exam 5: Inverse, Exponential, and Logarithmic Functions

Choose the one alternative that best completes the statement or answers the question. -A sample of 650 grams of radioactive substance decays according to the function $\mathrm { A } ( \mathrm { t } ) = 650 \mathrm { e } ^ { - .038 \mathrm { t } }$ , where $t$ is the time in years. How much of the substance will be left in the sample after 20 years? Round your answer to the nearest whole gram.

(Multiple Choice)

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Question 41

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $9 \mathrm { e } ^ { 2.1 \mathrm { x } } = 43$

(Multiple Choice)

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Question 42

Graph the function. Give the domain and range. - $f ( x ) = \log _ { 5 } x + 1$ $Graph the function. Give the domain and range. - f ( x ) = \log _ { 5 } x + 1$

(Multiple Choice)

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Question 43

For the function as defined that is one-to-one, graph f and $\mathbf { f } ^ { - 1 }$ on the same axes. - $f(x)=x^{2}-1$ $For the function as defined that is one-to-one, graph f and \mathbf { f } ^ { - 1 } on the same axes. - f(x)=x^{2}-1$

(Multiple Choice)

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Question 44

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $2 - x = 5 ^ { - x }$

(Multiple Choice)

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Question 45

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

(Multiple Choice)

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Question 46

Use properties of logarithms to evaluate the expression. - $1000 ^ { \log _ { 10 } 10 }$

(Multiple Choice)

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Question 47

Write an equivalent expression in exponential form. - $x = \log _ { 10 } 0.0001$

(Multiple Choice)

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Question 48

Choose the one alternative that best completes the statement or answers the question. -A population is increasing according to the exponential function defined by y $y = 3 e ^ { \cdot 04 x }$ , where y is in millions and x is the number of years. Which of the following should be done in order to answer The question "When will the population reach 4 million?"

(Multiple Choice)

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Question 49

Determine the function value. -Suppose $f ( x ) = \log _ { a } ( x )$ and $f ( 2 ) = 2$ . Find $f ( 8 )$ .

(Multiple Choice)

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Question 50

Write an equivalent expression in exponential form. - $\log 5125 = x$

(Multiple Choice)

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Question 51

Determine whether or not the function is one-to-one. - $f ( x ) = ( - 5 x - 5 ) ^ { 2 }$

(Multiple Choice)

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Question 52

Solve the equation. - $4 ^ { ( 7 - 3 x ) } = \frac { 1 } { 16 }$

(Multiple Choice)

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Question 53

Solve the equation and express the solution in exact form. - $\log _ { 8 } x = \sqrt { \log 8 x }$

(Multiple Choice)

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Question 54

Evaluate the logarithm. - $\log _ { 10 } 1000$

(Multiple Choice)

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Question 55

Choose the one alternative that best completes the statement or answers the question. -Suppose that $y = \frac { 2 - \log ( 100 - x ) } { 0.33 }$ can be used to calculate the number of years $y$ for $x$ percent of a population of 680 web-footed sparrows to die. Approximate the percentage (to the nearest whole per cent) of web-footed sparrows that died after 3 years.

(Multiple Choice)

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Question 56

Graph the exponential function using transformations where appropriate. - $f ( x ) = 2 ^ { x - 2 }$ $Graph the exponential function using transformations where appropriate. - f ( x ) = 2 ^ { x - 2 }$

(Multiple Choice)

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Question 57

Write the word or phrase that best completes each statement or answers the question. -Explain the error in the following: $\log _ { 4 } 3 \mathrm { y } = \log _ { 4 } 3 \cdot \log _ { 4 } \mathrm { y }$

(Essay)

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Question 58

Solve the problem. -An earthquake had an intensity $10 ^ { 4.4 }$ times more powerful than a reference level earthquake, or $104.4 \cdot \mathrm { I } _ { 0 }$ . What was the magnitude of this earthquake on the Richter scale? $\mathrm { R } = \log _ { 10 } \left( \mathrm { I } / \mathrm { I } _ { 0 } \right)$ .

(Multiple Choice)

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Question 59

Choose the one alternative that best completes the statement or answers the question. -A certain radioactive isotope has a half-life of approximately 1250 years. How many years to the nearest year would be required for a given amount of this isotope to decay to $70 \%$ of that amount?

(Multiple Choice)

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Question 60

Showing 41 - 60 of 472

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $9 \mathrm { e } ^ { 2.1 \mathrm { x } } = 43$

Graph the function. Give the domain and range. - $f ( x ) = \log _ { 5 } x + 1$ $Graph the function. Give the domain and range. - f ( x ) = \log _ { 5 } x + 1$

For the function as defined that is one-to-one, graph f and $\mathbf { f } ^ { - 1 }$ on the same axes. - $f(x)=x^{2}-1$ $For the function as defined that is one-to-one, graph f and \mathbf { f } ^ { - 1 } on the same axes. - f(x)=x^{2}-1$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $2 - x = 5 ^ { - x }$

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

Use properties of logarithms to evaluate the expression. - $1000 ^ { \log _ { 10 } 10 }$

Write an equivalent expression in exponential form. - $x = \log _ { 10 } 0.0001$

Determine the function value. -Suppose $f ( x ) = \log _ { a } ( x )$ and $f ( 2 ) = 2$ . Find $f ( 8 )$ .

Write an equivalent expression in exponential form. - $\log 5125 = x$

Determine whether or not the function is one-to-one. - $f ( x ) = ( - 5 x - 5 ) ^ { 2 }$

Solve the equation. - $4 ^ { ( 7 - 3 x ) } = \frac { 1 } { 16 }$

Solve the equation and express the solution in exact form. - $\log _ { 8 } x = \sqrt { \log 8 x }$

Evaluate the logarithm. - $\log _ { 10 } 1000$

Graph the exponential function using transformations where appropriate. - $f ( x ) = 2 ^ { x - 2 }$ $Graph the exponential function using transformations where appropriate. - f ( x ) = 2 ^ { x - 2 }$

Write the word or phrase that best completes each statement or answers the question. -Explain the error in the following: $\log _ { 4 } 3 \mathrm { y } = \log _ { 4 } 3 \cdot \log _ { 4 } \mathrm { y }$

Choose the one alternative that best completes the statement or answers the question. -A certain radioactive isotope has a half-life of approximately 1250 years. How many years to the nearest year would be required for a given amount of this isotope to decay to $70 \%$ of that amount?

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

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Exam 5: Inverse, Exponential, and Logarithmic Functions

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - 9e2.1x=439 \mathrm { e } ^ { 2.1 \mathrm { x } } = 439e2.1x=43

Graph the function. Give the domain and range. - f(x)=log⁡5x+1f ( x ) = \log _ { 5 } x + 1f(x)=log5​x+1

For the function as defined that is one-to-one, graph f and f−1\mathbf { f } ^ { - 1 }f−1 on the same axes. - f(x)=x2−1f(x)=x^{2}-1f(x)=x2−1

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - 2−x=5−x2 - x = 5 ^ { - x }2−x=5−x

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

Use properties of logarithms to evaluate the expression. - 1000log⁡10101000 ^ { \log _ { 10 } 10 }1000log10​10

Write an equivalent expression in exponential form. - x=log⁡100.0001x = \log _ { 10 } 0.0001x=log10​0.0001

Determine the function value. -Suppose f(x)=log⁡a(x)f ( x ) = \log _ { a } ( x )f(x)=loga​(x) and f(2)=2f ( 2 ) = 2f(2)=2 . Find f(8)f ( 8 )f(8) .

Write an equivalent expression in exponential form. - log⁡5125=x\log 5125 = xlog5125=x

Determine whether or not the function is one-to-one. - f(x)=(−5x−5)2f ( x ) = ( - 5 x - 5 ) ^ { 2 }f(x)=(−5x−5)2

Solve the equation. - 4(7−3x)=1164 ^ { ( 7 - 3 x ) } = \frac { 1 } { 16 }4(7−3x)=161​

Solve the equation and express the solution in exact form. - log⁡8x=log⁡8x\log _ { 8 } x = \sqrt { \log 8 x }log8​x=log8x​

Evaluate the logarithm. - log⁡101000\log _ { 10 } 1000log10​1000

Graph the exponential function using transformations where appropriate. - f(x)=2x−2f ( x ) = 2 ^ { x - 2 }f(x)=2x−2

Write the word or phrase that best completes each statement or answers the question. -Explain the error in the following: log⁡43y=log⁡43⋅log⁡4y\log _ { 4 } 3 \mathrm { y } = \log _ { 4 } 3 \cdot \log _ { 4 } \mathrm { y }log4​3y=log4​3⋅log4​y

Choose the one alternative that best completes the statement or answers the question. -A certain radioactive isotope has a half-life of approximately 1250 years. How many years to the nearest year would be required for a given amount of this isotope to decay to 70%70 \%70% of that amount?

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $9 \mathrm { e } ^ { 2.1 \mathrm { x } } = 43$

Graph the function. Give the domain and range. - $f ( x ) = \log _ { 5 } x + 1$ $Graph the function. Give the domain and range. - f ( x ) = \log _ { 5 } x + 1$

For the function as defined that is one-to-one, graph f and $\mathbf { f } ^ { - 1 }$ on the same axes. - $f(x)=x^{2}-1$ $For the function as defined that is one-to-one, graph f and \mathbf { f } ^ { - 1 } on the same axes. - f(x)=x^{2}-1$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $2 - x = 5 ^ { - x }$

Use properties of logarithms to evaluate the expression. - $1000 ^ { \log _ { 10 } 10 }$

Write an equivalent expression in exponential form. - $x = \log _ { 10 } 0.0001$

Determine the function value. -Suppose $f ( x ) = \log _ { a } ( x )$ and $f ( 2 ) = 2$ . Find $f ( 8 )$ .

Write an equivalent expression in exponential form. - $\log 5125 = x$

Determine whether or not the function is one-to-one. - $f ( x ) = ( - 5 x - 5 ) ^ { 2 }$

Solve the equation. - $4 ^ { ( 7 - 3 x ) } = \frac { 1 } { 16 }$

Solve the equation and express the solution in exact form. - $\log _ { 8 } x = \sqrt { \log 8 x }$

Evaluate the logarithm. - $\log _ { 10 } 1000$

Graph the exponential function using transformations where appropriate. - $f ( x ) = 2 ^ { x - 2 }$ $Graph the exponential function using transformations where appropriate. - f ( x ) = 2 ^ { x - 2 }$

Write the word or phrase that best completes each statement or answers the question. -Explain the error in the following: $\log _ { 4 } 3 \mathrm { y } = \log _ { 4 } 3 \cdot \log _ { 4 } \mathrm { y }$

Choose the one alternative that best completes the statement or answers the question. -A certain radioactive isotope has a half-life of approximately 1250 years. How many years to the nearest year would be required for a given amount of this isotope to decay to $70 \%$ of that amount?