Exam 9: Exponential and Logarithmic Functions

Use the function of $f ( x ) = \{ ( - 2,3 ) , ( - 1,1 ) , ( 0,0 ) , ( 1 , - 1 ) , ( 2 , - 3 ) \}$ and $g ( x ) = \{ ( - 3 , - 2 ) , ( - 1 , - 3 ) , ( 0,3 ) , ( 2,4 ) , ( 3,4 ) \}$ to find the value of $( g \circ f ) ( - 2 )$ .

(Multiple Choice)

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Question 101

Solve the logarithmic equation. Round your answer to two decimal places. $\log _ { 2 } x + \log _ { 2 } ( x + 1 ) - \log _ { 2 } 3 = 4$

(Multiple Choice)

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Question 102

Which statement(s)verify that $f ( x ) = \frac { 4 } { x + 1 }$ and $g ( x ) = \frac { 4 - x } { x }$ are inverse?

(Multiple Choice)

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Question 103

Determine the principal P (to the nearest cent)that will yield a balance of $A = 500,000$ dollars when invested at rate $r = 8.5 \%$ for 40 years, compounded continuously. Round the answer to two decimal places.

(Multiple Choice)

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Question 104

Simplify the expression. $\left( 4 e ^ { x } \right) ^ { 3 }$

(Multiple Choice)

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Question 105

A sport utility vehicle that costs $33,000 new has a depreciated value of $22,000 after 1 year. Find the value of the sport utility vehicle when it is 3 years old by using the exponential model $y = C e ^ { k t }$ . Round your answer to the nearest dollar.

(Multiple Choice)

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Question 106

An investment of $500 is made in a trust fund at an annual interest rate of 5%, compounded monthly. How long will it take for the investment to double? Give your answer to two decimal places.

(Multiple Choice)

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Question 107

Determine the balance A ( to the nearest cent)for P=3,000 dollars invested at a rate r=9% for t=10 , compounded 365 times per year. Round the answer to two decimal places.

(Multiple Choice)

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Question 108

The antler spread a (in inches)and should height h (in inches)of an adult male American elk are related by the model $h = 116 \log _ { 10 } ( a + 40 ) - 176$ . Approximate (to the nearest inch)the shoulder height of a male American elk with an antler spread of 52 inches.

(Multiple Choice)

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Question 109

You deposit $2000 in an account. At the end of 21 years, your balance is $10671.45. The bank tells you that the annual interest rate for the account is 8%. How is the interest compounded?

(Multiple Choice)

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Question 110

Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function. $Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function. f ( x ) = 5 \sqrt { - x }$ $f ( x ) = 5 \sqrt { - x }$

(Multiple Choice)

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Question 111

Find the inverse function of $f ( t ) = t ^ { 7 } - 5$ .

(Multiple Choice)

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Question 112

Determine the balance A ( to the nearest cent)for P=3,000 dollars invested at a rate r=10% for t=10 , compounded continuously. Round the answer to two decimal places.

(Multiple Choice)

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Question 113

Use the properties of logarithms to expand $\ln \sqrt { \frac { 2 x } { x - 6 } }$ .

(Multiple Choice)

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Question 114

Find $( f \circ g ) ( 4 )$ where $f ( x ) = 5 x + 9$ and $g ( x ) = x - 5$ .

(Multiple Choice)

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Question 115

Identify the horizontal asymptote of $h ( x ) = \frac { 1 } { 2 } \left( 15 ^ { - x } \right)$ .

(Multiple Choice)

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Question 116

Determine whether the value $x = \frac { 343 } { 8 }$ is a solution of the equation $\log _ { 49 } ( 8 x ) = \frac { 3 } { 2 }$ .

(Multiple Choice)

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Question 117

Solve the exponential equation. Round your answer to two decimal places. $6 \left( 1 + e ^ { \frac { x } { 3 } } \right) = 67$

(Multiple Choice)

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Question 118

Solve the exponential equation. Round your answer to two decimal places. $7 ^ { x + 3 } - 5 = 18$

(Multiple Choice)

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Question 119

Match $f ( x ) = 3 + \log _ { 5 } x$ with its graph.

(Multiple Choice)

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Question 120

Use the function of $f ( x ) = \{ ( - 2,3 ) , ( - 1,1 ) , ( 0,0 ) , ( 1 , - 1 ) , ( 2 , - 3 ) \}$ and $g ( x ) = \{ ( - 3 , - 2 ) , ( - 1 , - 3 ) , ( 0,3 ) , ( 2,4 ) , ( 3,4 ) \}$ to find the value of $( g \circ f ) ( - 2 )$ .

Solve the logarithmic equation. Round your answer to two decimal places. $\log _ { 2 } x + \log _ { 2 } ( x + 1 ) - \log _ { 2 } 3 = 4$

Which statement(s)verify that $f ( x ) = \frac { 4 } { x + 1 }$ and $g ( x ) = \frac { 4 - x } { x }$ are inverse?

Determine the principal P (to the nearest cent)that will yield a balance of $A = 500,000$ dollars when invested at rate $r = 8.5 \%$ for 40 years, compounded continuously. Round the answer to two decimal places.

Simplify the expression. $\left( 4 e ^ { x } \right) ^ { 3 }$

A sport utility vehicle that costs $33,000 new has a depreciated value of $22,000 after 1 year. Find the value of the sport utility vehicle when it is 3 years old by using the exponential model $y = C e ^ { k t }$ . Round your answer to the nearest dollar.

An investment of $500 is made in a trust fund at an annual interest rate of 5%, compounded monthly. How long will it take for the investment to double? Give your answer to two decimal places.

Determine the balance A ( to the nearest cent)for P=3,000 dollars invested at a rate r=9% for t=10 , compounded 365 times per year. Round the answer to two decimal places.

The antler spread a (in inches)and should height h (in inches)of an adult male American elk are related by the model $h = 116 \log _ { 10 } ( a + 40 ) - 176$ . Approximate (to the nearest inch)the shoulder height of a male American elk with an antler spread of 52 inches.

You deposit $2000 in an account. At the end of 21 years, your balance is $10671.45. The bank tells you that the annual interest rate for the account is 8%. How is the interest compounded?

Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function. $Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function. f ( x ) = 5 \sqrt { - x }$ $f ( x ) = 5 \sqrt { - x }$

Find the inverse function of $f ( t ) = t ^ { 7 } - 5$ .

Determine the balance A ( to the nearest cent)for P=3,000 dollars invested at a rate r=10% for t=10 , compounded continuously. Round the answer to two decimal places.

Use the properties of logarithms to expand $\ln \sqrt { \frac { 2 x } { x - 6 } }$ .

Find $( f \circ g ) ( 4 )$ where $f ( x ) = 5 x + 9$ and $g ( x ) = x - 5$ .

Identify the horizontal asymptote of $h ( x ) = \frac { 1 } { 2 } \left( 15 ^ { - x } \right)$ .

Determine whether the value $x = \frac { 343 } { 8 }$ is a solution of the equation $\log _ { 49 } ( 8 x ) = \frac { 3 } { 2 }$ .

Solve the exponential equation. Round your answer to two decimal places. $6 \left( 1 + e ^ { \frac { x } { 3 } } \right) = 67$

Solve the exponential equation. Round your answer to two decimal places. $7 ^ { x + 3 } - 5 = 18$

Match $f ( x ) = 3 + \log _ { 5 } x$ with its graph.

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Factoring

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Quadratic Equations, Functions, and Inequalities

Conics

Sequences, Series, and the Binomial Theorem

Filters

Exam 9: Exponential and Logarithmic Functions

Solve the logarithmic equation. Round your answer to two decimal places. log⁡2x+log⁡2(x+1)−log⁡23=4\log _ { 2 } x + \log _ { 2 } ( x + 1 ) - \log _ { 2 } 3 = 4log2​x+log2​(x+1)−log2​3=4

Which statement(s)verify that f(x)=4x+1f ( x ) = \frac { 4 } { x + 1 }f(x)=x+14​ and g(x)=4−xxg ( x ) = \frac { 4 - x } { x }g(x)=x4−x​ are inverse?

Determine the principal P (to the nearest cent)that will yield a balance of A=500,000A = 500,000A=500,000 dollars when invested at rate r=8.5%r = 8.5 \%r=8.5% for 40 years, compounded continuously. Round the answer to two decimal places.

Simplify the expression. (4ex)3\left( 4 e ^ { x } \right) ^ { 3 }(4ex)3

A sport utility vehicle that costs $33,000 new has a depreciated value of $22,000 after 1 year. Find the value of the sport utility vehicle when it is 3 years old by using the exponential model y=Cekty = C e ^ { k t }y=Cekt . Round your answer to the nearest dollar.

An investment of $500 is made in a trust fund at an annual interest rate of 5%, compounded monthly. How long will it take for the investment to double? Give your answer to two decimal places.

Determine the balance A ( to the nearest cent)for P=3,000 dollars invested at a rate r=9% for t=10 , compounded 365 times per year. Round the answer to two decimal places.

You deposit $2000 in an account. At the end of 21 years, your balance is $10671.45. The bank tells you that the annual interest rate for the account is 8%. How is the interest compounded?

Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function. f(x)=5−xf ( x ) = 5 \sqrt { - x }f(x)=5−x​

Find the inverse function of f(t)=t7−5f ( t ) = t ^ { 7 } - 5f(t)=t7−5 .

Determine the balance A ( to the nearest cent)for P=3,000 dollars invested at a rate r=10% for t=10 , compounded continuously. Round the answer to two decimal places.

Use the properties of logarithms to expand ln⁡2xx−6\ln \sqrt { \frac { 2 x } { x - 6 } }lnx−62x​​ .

Find (f∘g)(4)( f \circ g ) ( 4 )(f∘g)(4) where f(x)=5x+9f ( x ) = 5 x + 9f(x)=5x+9 and g(x)=x−5g ( x ) = x - 5g(x)=x−5 .

Identify the horizontal asymptote of h(x)=12(15−x)h ( x ) = \frac { 1 } { 2 } \left( 15 ^ { - x } \right)h(x)=21​(15−x) .

Determine whether the value x=3438x = \frac { 343 } { 8 }x=8343​ is a solution of the equation log⁡49(8x)=32\log _ { 49 } ( 8 x ) = \frac { 3 } { 2 }log49​(8x)=23​ .

Solve the exponential equation. Round your answer to two decimal places. 6(1+ex3)=676 \left( 1 + e ^ { \frac { x } { 3 } } \right) = 676(1+e3x​)=67

Solve the exponential equation. Round your answer to two decimal places. 7x+3−5=187 ^ { x + 3 } - 5 = 187x+3−5=18

Match f(x)=3+log⁡5xf ( x ) = 3 + \log _ { 5 } xf(x)=3+log5​x with its graph.

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Factoring

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Quadratic Equations, Functions, and Inequalities

Conics

Sequences, Series, and the Binomial Theorem

Filters

Solve the logarithmic equation. Round your answer to two decimal places. $\log _ { 2 } x + \log _ { 2 } ( x + 1 ) - \log _ { 2 } 3 = 4$

Which statement(s)verify that $f ( x ) = \frac { 4 } { x + 1 }$ and $g ( x ) = \frac { 4 - x } { x }$ are inverse?

Determine the principal P (to the nearest cent)that will yield a balance of $A = 500,000$ dollars when invested at rate $r = 8.5 \%$ for 40 years, compounded continuously. Round the answer to two decimal places.

Simplify the expression. $\left( 4 e ^ { x } \right) ^ { 3 }$

A sport utility vehicle that costs $33,000 new has a depreciated value of $22,000 after 1 year. Find the value of the sport utility vehicle when it is 3 years old by using the exponential model $y = C e ^ { k t }$ . Round your answer to the nearest dollar.

Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function. $Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function. f ( x ) = 5 \sqrt { - x }$ $f ( x ) = 5 \sqrt { - x }$

Find the inverse function of $f ( t ) = t ^ { 7 } - 5$ .

Use the properties of logarithms to expand $\ln \sqrt { \frac { 2 x } { x - 6 } }$ .

Find $( f \circ g ) ( 4 )$ where $f ( x ) = 5 x + 9$ and $g ( x ) = x - 5$ .

Identify the horizontal asymptote of $h ( x ) = \frac { 1 } { 2 } \left( 15 ^ { - x } \right)$ .

Determine whether the value $x = \frac { 343 } { 8 }$ is a solution of the equation $\log _ { 49 } ( 8 x ) = \frac { 3 } { 2 }$ .

Solve the exponential equation. Round your answer to two decimal places. $6 \left( 1 + e ^ { \frac { x } { 3 } } \right) = 67$

Solve the exponential equation. Round your answer to two decimal places. $7 ^ { x + 3 } - 5 = 18$

Match $f ( x ) = 3 + \log _ { 5 } x$ with its graph.