Exam 4: Exponential and Logarithmic Functions

The graph of a logarithmic function is shown. Select the function which matches the graph. - $The graph of a logarithmic function is shown. Select the function which matches the graph. - A) f ( x ) = \log _ { 5 } x B) f ( x ) = \log _ { 5 } ( x - 1 ) C) f ( x ) = \log _ { 5 } x - 1 D) f ( x ) = \log _ { 5 } ( x + 1 )$ A) $f ( x ) = \log _ { 5 } x$ B) $f ( x ) = \log _ { 5 } ( x - 1 )$ C) $f ( x ) = \log _ { 5 } x - 1$ D) $f ( x ) = \log _ { 5 } ( x + 1 )$

(Multiple Choice)

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Question 381

Use a calculator to find the natural logarithm correct to four decimal places. - $\ln \left( 3.64 \cdot 10 ^ { - 8 } \right)$

(Multiple Choice)

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Question 382

Solve the problem. -What principal invested at 8% compounded continuously for 4 years will yield $1190? Round the answer to two decimal places.

(Multiple Choice)

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Question 383

Use the horizontal line test to determine whether the function is one-to-one. -

(Multiple Choice)

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Question 384

Change the exponential expression to an equivalent expression involving a logarithm. - $3 ^ { - 2 } = \frac { 1 } { 9 }$

(Multiple Choice)

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Question 385

Solve the equation. - $2 ^ { ( 7 - 3 x ) } = \frac { 1 } { 4 }$

(Multiple Choice)

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Question 386

Solve the equation. -models the average number of free-throws a basketball player can make consecutively during practice as a function of time, where x is the number of consecutive days the basketball Player has practiced for two hours. After how many days of practice can the basketball player make an average Of 7 consecutive free throws?

(Multiple Choice)

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Question 387

Solve the equation. - $\log _ { 3 } ( 3 x + 7 ) = \log _ { 3 } ( 3 x + 2 )$

(Multiple Choice)

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Question 388

Find the domain of the composite function f $f ^ { \circ } g$ - $f ( x ) = \sqrt { x } ; \quad g ( x ) = 5 x + 10$

(Multiple Choice)

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Question 389

Solve the problem. -The logistic growth model $P ( t ) = \frac { 410 } { 1 + 40 e ^ { - 0.176 t } }$ represents the population of a species introduced into a new territory after t years. When will the population be 60?

(Multiple Choice)

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Question 390

Solve the problem. -The functio $\mathrm { A } = \mathrm { A } _ { \mathrm { O } } \mathrm { e } ^ { - 0.0099 \mathrm { x } }$ models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. If 500 pounds of the Material are initially put into the vault, how many pounds will be left after 80 years?

(Multiple Choice)

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Question 391

Solve the problem. -How long does it take $1125 to triple if it is invested at 7% interest, compounded quarterly? Round your answer to the nearest tenth.

(Multiple Choice)

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Question 392

Use a graphing calculator to solve the equation. Round your answer to two decimal places. - $\log _ { 4 } ( x + 2 ) - \log _ { 5 } ( x - 1 ) = 1$

(Multiple Choice)

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Question 393

Solve the equation. - $8 \ln 3 x = 40$

(Multiple Choice)

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Question 394

Decide whether or not the functions are inverses of each other. - $f ( x ) = \frac { 6 + x } { x } , g ( x ) = \frac { 6 } { x - 1 }$

(Multiple Choice)

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Question 395

Use the horizontal line test to determine whether the function is one-to-one. -

(Multiple Choice)

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Question 396

Solve the problem. -The logistic growth functi $f ( t ) = \frac { 440 } { 1 + 7.8 e ^ { - 0.17 t } }$ describes the population of a species of butterflies t months after they are introduced to a non-threatening habitat. How many butterflies were initially introduced to the Habitat?

(Multiple Choice)

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Question 397

Solve the problem. -The bacteria in a 8-liter container double every 3 minutes. After 57 minutes the container is full. How long did it take to fill a quarter of the container?

(Multiple Choice)

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Question 398

Graph the function. - $f(x)=4-e^{-x}$ $Graph the function. - f(x)=4-e^{-x} A) B) C) D)$ A) $Graph the function. - f(x)=4-e^{-x} A) B) C) D)$ B) $Graph the function. - f(x)=4-e^{-x} A) B) C) D)$ C) $Graph the function. - f(x)=4-e^{-x} A) B) C) D)$ D) $Graph the function. - f(x)=4-e^{-x} A) B) C) D)$

(Multiple Choice)

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Question 399

Change the logarithmic expression to an equivalent expression involving an exponent. - $\log _ { 1024 } 256 = \frac { 4 } { 5 }$

(Multiple Choice)

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Question 400

Showing 381 - 400 of 518

Use a calculator to find the natural logarithm correct to four decimal places. - $\ln \left( 3.64 \cdot 10 ^ { - 8 } \right)$

Solve the problem. -What principal invested at 8% compounded continuously for 4 years will yield $1190? Round the answer to two decimal places.

Use the horizontal line test to determine whether the function is one-to-one. -

Change the exponential expression to an equivalent expression involving a logarithm. - $3 ^ { - 2 } = \frac { 1 } { 9 }$

Solve the equation. - $2 ^ { ( 7 - 3 x ) } = \frac { 1 } { 4 }$

Solve the equation. - $\log _ { 3 } ( 3 x + 7 ) = \log _ { 3 } ( 3 x + 2 )$

Find the domain of the composite function f $f ^ { \circ } g$ - $f ( x ) = \sqrt { x } ; \quad g ( x ) = 5 x + 10$

Solve the problem. -The logistic growth model $P ( t ) = \frac { 410 } { 1 + 40 e ^ { - 0.176 t } }$ represents the population of a species introduced into a new territory after t years. When will the population be 60?

Solve the problem. -How long does it take $1125 to triple if it is invested at 7% interest, compounded quarterly? Round your answer to the nearest tenth.

Use a graphing calculator to solve the equation. Round your answer to two decimal places. - $\log _ { 4 } ( x + 2 ) - \log _ { 5 } ( x - 1 ) = 1$

Solve the equation. - $8 \ln 3 x = 40$

Decide whether or not the functions are inverses of each other. - $f ( x ) = \frac { 6 + x } { x } , g ( x ) = \frac { 6 } { x - 1 }$

Use the horizontal line test to determine whether the function is one-to-one. -

Solve the problem. -The logistic growth functi $f ( t ) = \frac { 440 } { 1 + 7.8 e ^ { - 0.17 t } }$ describes the population of a species of butterflies t months after they are introduced to a non-threatening habitat. How many butterflies were initially introduced to the Habitat?

Solve the problem. -The bacteria in a 8-liter container double every 3 minutes. After 57 minutes the container is full. How long did it take to fill a quarter of the container?

Graph the function. - $f(x)=4-e^{-x}$ $Graph the function. - f(x)=4-e^{-x} A) B) C) D)$ A) $Graph the function. - f(x)=4-e^{-x} A) B) C) D)$ B) $Graph the function. - f(x)=4-e^{-x} A) B) C) D)$ C) $Graph the function. - f(x)=4-e^{-x} A) B) C) D)$ D) $Graph the function. - f(x)=4-e^{-x} A) B) C) D)$

Change the logarithmic expression to an equivalent expression involving an exponent. - $\log _ { 1024 } 256 = \frac { 4 } { 5 }$

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

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Exam 4: Exponential and Logarithmic Functions

Use a calculator to find the natural logarithm correct to four decimal places. - ln⁡(3.64⋅10−8)\ln \left( 3.64 \cdot 10 ^ { - 8 } \right)ln(3.64⋅10−8)

Solve the problem. -What principal invested at 8% compounded continuously for 4 years will yield $1190? Round the answer to two decimal places.

Use the horizontal line test to determine whether the function is one-to-one. -

Change the exponential expression to an equivalent expression involving a logarithm. - 3−2=193 ^ { - 2 } = \frac { 1 } { 9 }3−2=91​

Solve the equation. - 2(7−3x)=142 ^ { ( 7 - 3 x ) } = \frac { 1 } { 4 }2(7−3x)=41​

Solve the equation. - log⁡3(3x+7)=log⁡3(3x+2)\log _ { 3 } ( 3 x + 7 ) = \log _ { 3 } ( 3 x + 2 )log3​(3x+7)=log3​(3x+2)

Find the domain of the composite function f f∘gf ^ { \circ } g f∘g - f(x)=x;g(x)=5x+10f ( x ) = \sqrt { x } ; \quad g ( x ) = 5 x + 10f(x)=x​;g(x)=5x+10

Solve the problem. -The logistic growth model P(t)=4101+40e−0.176tP ( t ) = \frac { 410 } { 1 + 40 e ^ { - 0.176 t } }P(t)=1+40e−0.176t410​ represents the population of a species introduced into a new territory after t years. When will the population be 60?

Solve the problem. -How long does it take $1125 to triple if it is invested at 7% interest, compounded quarterly? Round your answer to the nearest tenth.

Use a graphing calculator to solve the equation. Round your answer to two decimal places. - log⁡4(x+2)−log⁡5(x−1)=1\log _ { 4 } ( x + 2 ) - \log _ { 5 } ( x - 1 ) = 1log4​(x+2)−log5​(x−1)=1

Solve the equation. - 8ln⁡3x=408 \ln 3 x = 408ln3x=40

Decide whether or not the functions are inverses of each other. - f(x)=6+xx,g(x)=6x−1f ( x ) = \frac { 6 + x } { x } , g ( x ) = \frac { 6 } { x - 1 }f(x)=x6+x​,g(x)=x−16​

Use the horizontal line test to determine whether the function is one-to-one. -

Solve the problem. -The bacteria in a 8-liter container double every 3 minutes. After 57 minutes the container is full. How long did it take to fill a quarter of the container?

Graph the function. - f(x)=4−e−xf(x)=4-e^{-x}f(x)=4−e−x A) B) C) D)

Change the logarithmic expression to an equivalent expression involving an exponent. - log⁡1024256=45\log _ { 1024 } 256 = \frac { 4 } { 5 }log1024​256=54​

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Review

Filters

Use a calculator to find the natural logarithm correct to four decimal places. - $\ln \left( 3.64 \cdot 10 ^ { - 8 } \right)$

Change the exponential expression to an equivalent expression involving a logarithm. - $3 ^ { - 2 } = \frac { 1 } { 9 }$

Solve the equation. - $2 ^ { ( 7 - 3 x ) } = \frac { 1 } { 4 }$

Solve the equation. - $\log _ { 3 } ( 3 x + 7 ) = \log _ { 3 } ( 3 x + 2 )$

Find the domain of the composite function f $f ^ { \circ } g$ - $f ( x ) = \sqrt { x } ; \quad g ( x ) = 5 x + 10$

Solve the problem. -The logistic growth model $P ( t ) = \frac { 410 } { 1 + 40 e ^ { - 0.176 t } }$ represents the population of a species introduced into a new territory after t years. When will the population be 60?

Use a graphing calculator to solve the equation. Round your answer to two decimal places. - $\log _ { 4 } ( x + 2 ) - \log _ { 5 } ( x - 1 ) = 1$

Solve the equation. - $8 \ln 3 x = 40$

Decide whether or not the functions are inverses of each other. - $f ( x ) = \frac { 6 + x } { x } , g ( x ) = \frac { 6 } { x - 1 }$

Graph the function. - $f(x)=4-e^{-x}$ $Graph the function. - f(x)=4-e^{-x} A) B) C) D)$ A) $Graph the function. - f(x)=4-e^{-x} A) B) C) D)$ B) $Graph the function. - f(x)=4-e^{-x} A) B) C) D)$ C) $Graph the function. - f(x)=4-e^{-x} A) B) C) D)$ D) $Graph the function. - f(x)=4-e^{-x} A) B) C) D)$

Change the logarithmic expression to an equivalent expression involving an exponent. - $\log _ { 1024 } 256 = \frac { 4 } { 5 }$