Exam 12: Logarithmic and Exponential Functions

Solve. -One method to determine the time since an animal died is to estimate the percentage of carbon-14 remaining in its bones. The percent P in decimal form of carbon-14 remaining x years is given by P(x) = e-0.000121x. Approximate (to the nearest whole year) the age of a fossil if there is 65% of Carbon-14 remaining.

(Multiple Choice)

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Question 41

Rewrite as a single logarithm using the quotient rule for logarithms. Assume all variables represent positive real numbers. - $\log _ { a } 1,000,000 - \log _ { a } 1000$

(Multiple Choice)

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Question 42

Compute the compound interest. -How long must $4200 be in a bank at 6% compounded annually to become $7521.56? (Round to the nearest year.)

(Multiple Choice)

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Question 43

Evaluate. Round to the nearest thousandth, if necessary. - $\ln 223$

(Multiple Choice)

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Question 44

Solve the problem. -Yearly sales of an electronic device $S ( t )$ , in millions of dollars, $t$ years after 1997 can be estimated by $S ( t ) = 100 \cdot 6 ^ { t }$ . What is the doubling time for the yearly sales? Round your answer to the nearest tenth.

(Multiple Choice)

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Question 45

Solve the problem. -Find the hydrogen ion concentration of a solution [ $\left. \mathrm { H } ^ { + } \right]$ whose $\mathrm { pH }$ is $7.5$ . Use the formula $\mathrm { pH } = - \log \left[ \mathrm { H } ^ { + } \right]$ .

(Multiple Choice)

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Question 46

Rewrite using the power rule. Assume all variables represent positive real numbers. - $\log _ { 3 } y ^ { 8 }$

(Multiple Choice)

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Question 47

Evaluate. Round to the nearest thousandth, if necessary. - $\log 0.001$

(Multiple Choice)

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Question 48

Expand. Assume that all variables represent positive real numbers. - $\log _ { 3 } \left( \frac { \sqrt { x } } { 81 } \right)$

(Multiple Choice)

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Question 49

Find the missing number. Round to the nearest hundredth if necessary. - $13 ^ { ? } = 19$

(Multiple Choice)

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Question 50

Solve the problem. -Yearly sales of an electronic device S(t), in millions of dollars, t years after 1998 can be estimated by $S ( t ) = 200 \cdot 2 ^ { t }$

(Multiple Choice)

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Question 51

Rewrite as a single logarithm using the product rule for logarithms. Assume all variables represent positive real numbers. - $\log _ { 3 } 6 + \log _ { 3 } x$

(Multiple Choice)

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Question 52

Evaluate the given function. $Evaluate the given function. - f ( x ) = \log _ { 3 } x , f ( 81 )$ $Evaluate the given function. - f ( x ) = \log _ { 3 } x , f ( 81 )$ - $f ( x ) = \log _ { 3 } x , f ( 81 )$

(Multiple Choice)

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Question 53

Rewrite as a single logarithm. Assume all variables represent positive real numbers. - $\log _ { b } x ^ { 8 } - 2 \log b \sqrt { x }$

(Multiple Choice)

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Question 54

Rewrite as a single logarithm using the product rule for logarithms. Assume all variables represent positive real numbers. - $\log _ { 5 } x + \log _ { 5 } y$

(Multiple Choice)

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Question 55

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of this function. - $f ( x ) = \ln ( x + 2 ) - 4$

(Multiple Choice)

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Question 56

Find the missing number. Round to the nearest hundredth if necessary. - $21 ^ { ? } = 45$

(Multiple Choice)

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Question 57

Solve. -The function $\mathrm { A } = \mathrm { A } \cap \mathrm { e } ^ { - 0.0077 \mathrm { x } }$

(Multiple Choice)

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Question 58

Evaluate. Round to the nearest thousandth, if necessary. - $\ln \left( \frac { 1 } { e ^ { 5 } } \right)$

(Multiple Choice)

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Question 59

Evaluate. Round to the nearest thousandth, if necessary. - $\log 3.49$

(Multiple Choice)

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Question 60

Rewrite as a single logarithm using the quotient rule for logarithms. Assume all variables represent positive real numbers. - $\log _ { a } 1,000,000 - \log _ { a } 1000$

Compute the compound interest. -How long must $4200 be in a bank at 6% compounded annually to become $7521.56? (Round to the nearest year.)

Evaluate. Round to the nearest thousandth, if necessary. - $\ln 223$

Solve the problem. -Yearly sales of an electronic device $S ( t )$ , in millions of dollars, $t$ years after 1997 can be estimated by $S ( t ) = 100 \cdot 6 ^ { t }$ . What is the doubling time for the yearly sales? Round your answer to the nearest tenth.

Solve the problem. -Find the hydrogen ion concentration of a solution [ $\left. \mathrm { H } ^ { + } \right]$ whose $\mathrm { pH }$ is $7.5$ . Use the formula $\mathrm { pH } = - \log \left[ \mathrm { H } ^ { + } \right]$ .

Rewrite using the power rule. Assume all variables represent positive real numbers. - $\log _ { 3 } y ^ { 8 }$

Evaluate. Round to the nearest thousandth, if necessary. - $\log 0.001$

Expand. Assume that all variables represent positive real numbers. - $\log _ { 3 } \left( \frac { \sqrt { x } } { 81 } \right)$

Find the missing number. Round to the nearest hundredth if necessary. - $13 ^ { ? } = 19$

Solve the problem. -Yearly sales of an electronic device S(t), in millions of dollars, t years after 1998 can be estimated by $S ( t ) = 200 \cdot 2 ^ { t }$

Rewrite as a single logarithm using the product rule for logarithms. Assume all variables represent positive real numbers. - $\log _ { 3 } 6 + \log _ { 3 } x$

Evaluate the given function. $Evaluate the given function. - f ( x ) = \log _ { 3 } x , f ( 81 )$ $Evaluate the given function. - f ( x ) = \log _ { 3 } x , f ( 81 )$ - $f ( x ) = \log _ { 3 } x , f ( 81 )$

Rewrite as a single logarithm. Assume all variables represent positive real numbers. - $\log _ { b } x ^ { 8 } - 2 \log b \sqrt { x }$

Rewrite as a single logarithm using the product rule for logarithms. Assume all variables represent positive real numbers. - $\log _ { 5 } x + \log _ { 5 } y$

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of this function. - $f ( x ) = \ln ( x + 2 ) - 4$

Find the missing number. Round to the nearest hundredth if necessary. - $21 ^ { ? } = 45$

Solve. -The function $\mathrm { A } = \mathrm { A } \cap \mathrm { e } ^ { - 0.0077 \mathrm { x } }$

Evaluate. Round to the nearest thousandth, if necessary. - $\ln \left( \frac { 1 } { e ^ { 5 } } \right)$

Evaluate. Round to the nearest thousandth, if necessary. - $\log 3.49$

Review of Real Numbers

Linear Equations

Graphing Linear Equations

Systems of Equations

Exponents and Polynomials

Factoring and Quadratic Equations

Rational Expressions and Equations

A Transition

Radical Expressions and Equations

Quadratic Equations

Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 12: Logarithmic and Exponential Functions

Rewrite as a single logarithm using the quotient rule for logarithms. Assume all variables represent positive real numbers. - log⁡a1,000,000−log⁡a1000\log _ { a } 1,000,000 - \log _ { a } 1000loga​1,000,000−loga​1000

Compute the compound interest. -How long must $4200 be in a bank at 6% compounded annually to become $7521.56? (Round to the nearest year.)

Evaluate. Round to the nearest thousandth, if necessary. - ln⁡223\ln 223ln223

Solve the problem. -Yearly sales of an electronic device S(t)S ( t )S(t) , in millions of dollars, ttt years after 1997 can be estimated by S(t)=100⋅6tS ( t ) = 100 \cdot 6 ^ { t }S(t)=100⋅6t . What is the doubling time for the yearly sales? Round your answer to the nearest tenth.

Solve the problem. -Find the hydrogen ion concentration of a solution [ H+]\left. \mathrm { H } ^ { + } \right]H+] whose pH\mathrm { pH }pH is 7.57.57.5 . Use the formula pH=−log⁡[H+]\mathrm { pH } = - \log \left[ \mathrm { H } ^ { + } \right]pH=−log[H+] .

Rewrite using the power rule. Assume all variables represent positive real numbers. - log⁡3y8\log _ { 3 } y ^ { 8 }log3​y8

Evaluate. Round to the nearest thousandth, if necessary. - log⁡0.001\log 0.001log0.001

Expand. Assume that all variables represent positive real numbers. - log⁡3(x81)\log _ { 3 } \left( \frac { \sqrt { x } } { 81 } \right)log3​(81x​​)

Find the missing number. Round to the nearest hundredth if necessary. - 13?=1913 ^ { ? } = 1913?=19

Solve the problem. -Yearly sales of an electronic device S(t), in millions of dollars, t years after 1998 can be estimated by S(t)=200⋅2tS ( t ) = 200 \cdot 2 ^ { t }S(t)=200⋅2t

Rewrite as a single logarithm using the product rule for logarithms. Assume all variables represent positive real numbers. - log⁡36+log⁡3x\log _ { 3 } 6 + \log _ { 3 } xlog3​6+log3​x

Evaluate the given function. - f(x)=log⁡3x,f(81)f ( x ) = \log _ { 3 } x , f ( 81 )f(x)=log3​x,f(81)

Rewrite as a single logarithm. Assume all variables represent positive real numbers. - log⁡bx8−2log⁡bx\log _ { b } x ^ { 8 } - 2 \log b \sqrt { x }logb​x8−2logbx​

Rewrite as a single logarithm using the product rule for logarithms. Assume all variables represent positive real numbers. - log⁡5x+log⁡5y\log _ { 5 } x + \log _ { 5 } ylog5​x+log5​y

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of this function. - f(x)=ln⁡(x+2)−4f ( x ) = \ln ( x + 2 ) - 4f(x)=ln(x+2)−4

Find the missing number. Round to the nearest hundredth if necessary. - 21?=4521 ^ { ? } = 4521?=45

Solve. -The function A=A∩e−0.0077x\mathrm { A } = \mathrm { A } \cap \mathrm { e } ^ { - 0.0077 \mathrm { x } }A=A∩e−0.0077x

Evaluate. Round to the nearest thousandth, if necessary. - ln⁡(1e5)\ln \left( \frac { 1 } { e ^ { 5 } } \right)ln(e51​)

Evaluate. Round to the nearest thousandth, if necessary. - log⁡3.49\log 3.49log3.49

Review of Real Numbers

Linear Equations

Graphing Linear Equations

Systems of Equations

Exponents and Polynomials

Factoring and Quadratic Equations

Rational Expressions and Equations

A Transition

Radical Expressions and Equations

Quadratic Equations

Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Rewrite as a single logarithm using the quotient rule for logarithms. Assume all variables represent positive real numbers. - $\log _ { a } 1,000,000 - \log _ { a } 1000$

Evaluate. Round to the nearest thousandth, if necessary. - $\ln 223$

Solve the problem. -Yearly sales of an electronic device $S ( t )$ , in millions of dollars, $t$ years after 1997 can be estimated by $S ( t ) = 100 \cdot 6 ^ { t }$ . What is the doubling time for the yearly sales? Round your answer to the nearest tenth.

Solve the problem. -Find the hydrogen ion concentration of a solution [ $\left. \mathrm { H } ^ { + } \right]$ whose $\mathrm { pH }$ is $7.5$ . Use the formula $\mathrm { pH } = - \log \left[ \mathrm { H } ^ { + } \right]$ .

Rewrite using the power rule. Assume all variables represent positive real numbers. - $\log _ { 3 } y ^ { 8 }$

Evaluate. Round to the nearest thousandth, if necessary. - $\log 0.001$

Expand. Assume that all variables represent positive real numbers. - $\log _ { 3 } \left( \frac { \sqrt { x } } { 81 } \right)$

Find the missing number. Round to the nearest hundredth if necessary. - $13 ^ { ? } = 19$

Solve the problem. -Yearly sales of an electronic device S(t), in millions of dollars, t years after 1998 can be estimated by $S ( t ) = 200 \cdot 2 ^ { t }$

Rewrite as a single logarithm using the product rule for logarithms. Assume all variables represent positive real numbers. - $\log _ { 3 } 6 + \log _ { 3 } x$

Evaluate the given function. $Evaluate the given function. - f ( x ) = \log _ { 3 } x , f ( 81 )$ $Evaluate the given function. - f ( x ) = \log _ { 3 } x , f ( 81 )$ - $f ( x ) = \log _ { 3 } x , f ( 81 )$

Rewrite as a single logarithm. Assume all variables represent positive real numbers. - $\log _ { b } x ^ { 8 } - 2 \log b \sqrt { x }$

Rewrite as a single logarithm using the product rule for logarithms. Assume all variables represent positive real numbers. - $\log _ { 5 } x + \log _ { 5 } y$

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of this function. - $f ( x ) = \ln ( x + 2 ) - 4$

Find the missing number. Round to the nearest hundredth if necessary. - $21 ^ { ? } = 45$

Solve. -The function $\mathrm { A } = \mathrm { A } \cap \mathrm { e } ^ { - 0.0077 \mathrm { x } }$

Evaluate. Round to the nearest thousandth, if necessary. - $\ln \left( \frac { 1 } { e ^ { 5 } } \right)$

Evaluate. Round to the nearest thousandth, if necessary. - $\log 3.49$