Exam 9: Exponential and Logarithmic Functions

Determine the balance A ( to the nearest cent)for P=2,500 dollars invested at a rate r=9.5% for t=10 , compounded 4 times per year. Round the answer to two decimal places.

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(Multiple Choice)

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Question 1

Correct Answer:

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E

Solve the exponential equation. Round your answer to two decimal places. $7 ^ { x } = 119$

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(Multiple Choice)

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Question 2

Correct Answer:

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C

Match the graph with the graph of its inverse function.

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(Multiple Choice)

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Question 3

Correct Answer:

Verified

B

Solve the logarithmic equation. Round your answer to two decimal places. $\ln ( 0.8 x ) = \frac { 1 } { 5 }$

(Multiple Choice)

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Question 4

Write the exponential equation $729 ^ { 2 / 3 } = 81$ in logarithmic form.

(Multiple Choice)

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Question 5

In 1990, $88 million was paid for a painting. The same painting was sold for $53.0 million in 1987. Assume that the value of the painting increases at an exponential rate. When will the value of the painting be $100 million? Round your answer to two decimal places.

(Multiple Choice)

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Question 6

Determine the principal P (to the nearest cent)that will yield a balance of $A = 2,500,000$ dollars when invested at rate $r = 10 \%$ for 40 years, compounded 365 times per year. Round the answer to two decimal places.

(Multiple Choice)

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Question 7

Use the properties of logarithms to evaluate $\log _ { 5 } 75 - \log _ { 5 } 3$ without a calculator.

(Multiple Choice)

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Question 8

Use $\ln 6 \approx 1.7918$ , $\ln 10 \approx 2.3026$ , and the properties of logarithms to approximate $\ln \sqrt { 60 }$ to four decimal places.

(Multiple Choice)

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Question 9

Which statement(s)verify that $f ( x ) = 9 x - 1$ and $g ( x ) = \frac { 1 } { 9 } ( x + 1 )$ are inverse?

(Multiple Choice)

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Question 10

Write the logarithmic equation $\log _ { 2 } \frac { 1 } { 32 } = - 5$ in exponential form.

(Multiple Choice)

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Question 11

Use $\log _ { 16 } 4 = 0.5000$ , $\log _ { 16 } 3 \approx 0.3962$ , and the properties of logarithms to approximate $\log _ { 16 } \frac { 3 } { 4 }$ to four decimal places. Do not use a calculator.

(Multiple Choice)

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Question 12

Sketch the graph of the function $f ( x ) = 8 ^ { - x }$ .

(Multiple Choice)

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Question 13

Find $( g \circ f ) ( - 5 )$ where $f ( x ) = 3 x + 4$ and $g ( x ) = x ^ { 2 } - 6$ .

(Multiple Choice)

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Question 14

Use the properties of logarithms to expand $\ln 6 y$ .

(Multiple Choice)

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Question 15

Find the domain of $f \circ g$ where $f ( x ) = \sqrt { x - 7 }$ and $g ( x ) = x + 5$ .

(Multiple Choice)

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Question 16

Evaluate the logarithm. $\log _ { 3 } [ 27 ]$

(Multiple Choice)

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Question 17

Match $f ( x ) = \log _ { 4 } ( - x )$ with its graph.

(Multiple Choice)

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Question 18

Find the principal that must be deposited in an account with an annual interest rate of 4%, compounded monthly, so that after 15 years the balance is $4,000. Round your answer to the nearest cent.

(Multiple Choice)

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Question 19

Determine the principal P (to the nearest cent)that will yield a balance of $A = 500,000$ dollars when invested at rate $r = 6.5 \%$ for 40 years, compounded 12 times per year. Round the answer to two decimal places.

(Multiple Choice)

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Question 20

Determine the balance A ( to the nearest cent)for P=2,500 dollars invested at a rate r=9.5% for t=10 , compounded 4 times per year. Round the answer to two decimal places.

Solve the exponential equation. Round your answer to two decimal places. $7 ^ { x } = 119$

Match the graph with the graph of its inverse function.

Solve the logarithmic equation. Round your answer to two decimal places. $\ln ( 0.8 x ) = \frac { 1 } { 5 }$

Write the exponential equation $729 ^ { 2 / 3 } = 81$ in logarithmic form.

In 1990, $88 million was paid for a painting. The same painting was sold for $53.0 million in 1987. Assume that the value of the painting increases at an exponential rate. When will the value of the painting be $100 million? Round your answer to two decimal places.

Determine the principal P (to the nearest cent)that will yield a balance of $A = 2,500,000$ dollars when invested at rate $r = 10 \%$ for 40 years, compounded 365 times per year. Round the answer to two decimal places.

Use the properties of logarithms to evaluate $\log _ { 5 } 75 - \log _ { 5 } 3$ without a calculator.

Use $\ln 6 \approx 1.7918$ , $\ln 10 \approx 2.3026$ , and the properties of logarithms to approximate $\ln \sqrt { 60 }$ to four decimal places.

Which statement(s)verify that $f ( x ) = 9 x - 1$ and $g ( x ) = \frac { 1 } { 9 } ( x + 1 )$ are inverse?

Write the logarithmic equation $\log _ { 2 } \frac { 1 } { 32 } = - 5$ in exponential form.

Use $\log _ { 16 } 4 = 0.5000$ , $\log _ { 16 } 3 \approx 0.3962$ , and the properties of logarithms to approximate $\log _ { 16 } \frac { 3 } { 4 }$ to four decimal places. Do not use a calculator.

Sketch the graph of the function $f ( x ) = 8 ^ { - x }$ .

Find $( g \circ f ) ( - 5 )$ where $f ( x ) = 3 x + 4$ and $g ( x ) = x ^ { 2 } - 6$ .

Use the properties of logarithms to expand $\ln 6 y$ .

Find the domain of $f \circ g$ where $f ( x ) = \sqrt { x - 7 }$ and $g ( x ) = x + 5$ .

Evaluate the logarithm. $\log _ { 3 } [ 27 ]$

Match $f ( x ) = \log _ { 4 } ( - x )$ with its graph.

Find the principal that must be deposited in an account with an annual interest rate of 4%, compounded monthly, so that after 15 years the balance is $4,000. Round your answer to the nearest cent.

Determine the principal P (to the nearest cent)that will yield a balance of $A = 500,000$ dollars when invested at rate $r = 6.5 \%$ for 40 years, compounded 12 times per year. Round the answer to two decimal places.

Fundamentals of Algebra

Linear Equations and Inequalities

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Systems of Equations and Inequalities

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Exam 9: Exponential and Logarithmic Functions

Determine the balance A ( to the nearest cent)for P=2,500 dollars invested at a rate r=9.5% for t=10 , compounded 4 times per year. Round the answer to two decimal places.

Solve the exponential equation. Round your answer to two decimal places. 7x=1197 ^ { x } = 1197x=119

Match the graph with the graph of its inverse function.

Solve the logarithmic equation. Round your answer to two decimal places. ln⁡(0.8x)=15\ln ( 0.8 x ) = \frac { 1 } { 5 }ln(0.8x)=51​

Write the exponential equation 7292/3=81729 ^ { 2 / 3 } = 817292/3=81 in logarithmic form.

In 1990, $88 million was paid for a painting. The same painting was sold for $53.0 million in 1987. Assume that the value of the painting increases at an exponential rate. When will the value of the painting be $100 million? Round your answer to two decimal places.

Determine the principal P (to the nearest cent)that will yield a balance of A=2,500,000A = 2,500,000A=2,500,000 dollars when invested at rate r=10%r = 10 \%r=10% for 40 years, compounded 365 times per year. Round the answer to two decimal places.

Use the properties of logarithms to evaluate log⁡575−log⁡53\log _ { 5 } 75 - \log _ { 5 } 3log5​75−log5​3 without a calculator.

Use ln⁡6≈1.7918\ln 6 \approx 1.7918ln6≈1.7918 , ln⁡10≈2.3026\ln 10 \approx 2.3026ln10≈2.3026 , and the properties of logarithms to approximate ln⁡60\ln \sqrt { 60 }ln60​ to four decimal places.

Which statement(s)verify that f(x)=9x−1f ( x ) = 9 x - 1f(x)=9x−1 and g(x)=19(x+1)g ( x ) = \frac { 1 } { 9 } ( x + 1 )g(x)=91​(x+1) are inverse?

Write the logarithmic equation log⁡2132=−5\log _ { 2 } \frac { 1 } { 32 } = - 5log2​321​=−5 in exponential form.

Use log⁡164=0.5000\log _ { 16 } 4 = 0.5000log16​4=0.5000 , log⁡163≈0.3962\log _ { 16 } 3 \approx 0.3962log16​3≈0.3962 , and the properties of logarithms to approximate log⁡1634\log _ { 16 } \frac { 3 } { 4 }log16​43​ to four decimal places. Do not use a calculator.

Sketch the graph of the function f(x)=8−xf ( x ) = 8 ^ { - x }f(x)=8−x .

Find (g∘f)(−5)( g \circ f ) ( - 5 )(g∘f)(−5) where f(x)=3x+4f ( x ) = 3 x + 4f(x)=3x+4 and g(x)=x2−6g ( x ) = x ^ { 2 } - 6g(x)=x2−6 .

Use the properties of logarithms to expand ln⁡6y\ln 6 yln6y .

Find the domain of f∘gf \circ gf∘g where f(x)=x−7f ( x ) = \sqrt { x - 7 }f(x)=x−7​ and g(x)=x+5g ( x ) = x + 5g(x)=x+5 .

Evaluate the logarithm. log⁡3[27]\log _ { 3 } [ 27 ]log3​[27]

Match f(x)=log⁡4(−x)f ( x ) = \log _ { 4 } ( - x )f(x)=log4​(−x) with its graph.

Find the principal that must be deposited in an account with an annual interest rate of 4%, compounded monthly, so that after 15 years the balance is $4,000. Round your answer to the nearest cent.

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=6.5%r = 6.5 \%r=6.5% for 40 years, compounded 12 times per year. Round the answer to two decimal places.

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 exponential equation. Round your answer to two decimal places. $7 ^ { x } = 119$

Solve the logarithmic equation. Round your answer to two decimal places. $\ln ( 0.8 x ) = \frac { 1 } { 5 }$

Write the exponential equation $729 ^ { 2 / 3 } = 81$ in logarithmic form.

Determine the principal P (to the nearest cent)that will yield a balance of $A = 2,500,000$ dollars when invested at rate $r = 10 \%$ for 40 years, compounded 365 times per year. Round the answer to two decimal places.

Use the properties of logarithms to evaluate $\log _ { 5 } 75 - \log _ { 5 } 3$ without a calculator.

Use $\ln 6 \approx 1.7918$ , $\ln 10 \approx 2.3026$ , and the properties of logarithms to approximate $\ln \sqrt { 60 }$ to four decimal places.

Which statement(s)verify that $f ( x ) = 9 x - 1$ and $g ( x ) = \frac { 1 } { 9 } ( x + 1 )$ are inverse?

Write the logarithmic equation $\log _ { 2 } \frac { 1 } { 32 } = - 5$ in exponential form.

Use $\log _ { 16 } 4 = 0.5000$ , $\log _ { 16 } 3 \approx 0.3962$ , and the properties of logarithms to approximate $\log _ { 16 } \frac { 3 } { 4 }$ to four decimal places. Do not use a calculator.

Sketch the graph of the function $f ( x ) = 8 ^ { - x }$ .

Find $( g \circ f ) ( - 5 )$ where $f ( x ) = 3 x + 4$ and $g ( x ) = x ^ { 2 } - 6$ .

Use the properties of logarithms to expand $\ln 6 y$ .

Find the domain of $f \circ g$ where $f ( x ) = \sqrt { x - 7 }$ and $g ( x ) = x + 5$ .

Evaluate the logarithm. $\log _ { 3 } [ 27 ]$

Match $f ( x ) = \log _ { 4 } ( - x )$ with its graph.

Determine the principal P (to the nearest cent)that will yield a balance of $A = 500,000$ dollars when invested at rate $r = 6.5 \%$ for 40 years, compounded 12 times per year. Round the answer to two decimal places.