Complete the table for a savings account in which interest is compounded continuously. \[\begin{array} { | c | c | c | c | } \hline \text { Initial investment } & \text { Annual rate } & \text { Time to double } & \text { Amount after 10 years } \\ \hline ....&5.78 \% & .... & \$ 10694.82 \\ \hline \end{array}\] (Round the answer up to two decimal places. )

A) Initial investment: $\$ 10000$ Time to double: 13 yr B) Initial investment: $\$ 9000$ Time to double: 10 yr C) Initial investment: $\$ 7000$ Time to double: 12 yr D) Initial investment: $\$ 6,000$ Time to double: 12 yr E) Initial investment: $\$ 8000$ Time to double: 12 yr A) Initial investment: $\$ 10000$ Time to double: 13 yr B) Initial investment: $\$ 9000$ Time to double: 10 yr C) Initial investment: $\$ 7000$ Time to double: 12 yr D) Initial investment: $\$ 6,000$ Time to double: 12 yr E) Initial investment: $\$ 8000$ Time to double: 12 yr

Сomplete the table for the radioactive isotope. \[\begin{array} { | c | c | c | c | } \hline \text { Isotope } & \begin{array} { c } \text { Half-life } \\ \text { (years) } \end{array} & \text { Initial Quantity } & \begin{array} { c } \text { Amount after } 1000 \\ \text { years } \end{array} \\ \hline { } ^ { 14 } \mathrm { C } & 5715 & --& 2 \mathrm {~g} \\ \hline \end{array}\]

A) Initial Quantity: $2.26 \mathrm {~g}$ B) Initial Quantity: $3.26 \mathrm {~g}$ C) Initial Quantity: $5.26 \mathrm {~g}$ D) Initial Quantity: $4.26 \mathrm {~g}$ E) Initial Quantity: $6.26 \mathrm {~g}$ A) Initial Quantity: $2.26 \mathrm {~g}$ B) Initial Quantity: $3.26 \mathrm {~g}$ C) Initial Quantity: $5.26 \mathrm {~g}$ D) Initial Quantity: $4.26 \mathrm {~g}$ E) Initial Quantity: $6.26 \mathrm {~g}$

Complete the table for the radioactive isotope.Round your answer to two decimal places.$\begin{array}{|l|l|l|l|} \hline \text { Isotope } & \begin{array}{l} \text { Half-life } \\ \text { (years) } \end{array} & \text { Initial Quantity } & \text { Amount after } 1000 \\ \hline{ }^{14} \mathrm{C} & 5715& 5 g & --\\ \hline \end{array}$

A) Amount after 1000 years: $5.43 \mathrm {~g}$ B) Amount after 1000 years: $6.43 \mathrm {~g}$ C) Amount after 1000 years: $4.43 \mathrm {~g}$ D) Amount after 1000 years: $7.43 \mathrm {~g}$ E) Amount after 1000 years: $8.43 \mathrm {~g}$ A) Amount after 1000 years: $5.43 \mathrm {~g}$ B) Amount after 1000 years: $6.43 \mathrm {~g}$ C) Amount after 1000 years: $4.43 \mathrm {~g}$ D) Amount after 1000 years: $7.43 \mathrm {~g}$ E) Amount after 1000 years: $8.43 \mathrm {~g}$

Complete the table for a savings account in which interest is compounded continuously. \[\begin{array} { | c | c | c | c | } \hline \text { Initial investment } & \text { Annual rate } & \text { Time to double } & \text { Amount after 10 years } \\ \hline \$7,000& \ldots& \ldots & \$ 13143.27 \\ \hline \end{array}\] (Round the answer up to two decimal places. )

A) Annual rate: $6.3 \%$ Time to double: 14 yr B) Annual rate: $6.3 \%$ Time to double: 11 yr C) Annual rate: $10.3 \%$ Time to double: 11 yr D) Annual rate: $8.3 \%$ Time to double: 11 yr E) Annual rate: $6.3 \%$ Time to double: 15 yr A) Annual rate: $6.3 \%$ Time to double: 14 yr B) Annual rate: $6.3 \%$ Time to double: 11 yr C) Annual rate: $10.3 \%$ Time to double: 11 yr D) Annual rate: $8.3 \%$ Time to double: 11 yr E) Annual rate: $6.3 \%$ Time to double: 15 yr

Find the exponential model $y = a e ^ { b x }$ that fits the points shown in the table. \[\begin{array} { | c | c | c | } \hline x & 0 & 3 \\ \hline y & 6 & 1.5 \\ \hline \end{array}\]

A) $y = \frac { 1 } { 2 } e ^ { 0.6621 x }$ B) $y = e ^ { - 0.5621 x }$ C) $y = - e ^ { 0.4621 x }$ D) $y = 6 e ^ { - 0.4621 x }$ E) $y = 2 e ^ { 0.4621 x }$ A) $y = \frac { 1 } { 2 } e ^ { 0.6621 x }$ B) $y = e ^ { - 0.5621 x }$ C) $y = - e ^ { 0.4621 x }$ D) $y = 6 e ^ { - 0.4621 x }$ E) $y = 2 e ^ { 0.4621 x }$

Complete the table for a savings account in which interest is compounded continuously. \[\begin{array} { | c | c | c | c | } \hline \text { Initial investment } & \text { Annual rate } & \text { Time to double } & \begin{array} { c } \text { Amount after 10 } \\ \text { years } \end{array} \\ \hline \$ 9,000 & \ldots & 13 \mathrm { yr } & \cdots \\ \hline \end{array}\] (Round the answer up to two decimal places. )

A) Annual rate: $5.33 \%$ Amount after 10 years: $\$ 14,836.33$ B) Annual rate: $5.33 \%$ Amount after 10 years: $\$ 15,836.33$ C) Annual rate: $5.33 \%$ Amount after 10 years: $\$ 15336.33$ D) Annual rate: $9.33 \%$ Amount after 10 years: $\$ 15336.33$ E) Annual rate: $7.33 \%$ Amount after 10 years: $\$ 15336.33$ A) Annual rate: $5.33 \%$ Amount after 10 years: $\$ 14,836.33$ B) Annual rate: $5.33 \%$ Amount after 10 years: $\$ 15,836.33$ C) Annual rate: $5.33 \%$ Amount after 10 years: $\$ 15336.33$ D) Annual rate: $9.33 \%$ Amount after 10 years: $\$ 15336.33$ E) Annual rate: $7.33 \%$ Amount after 10 years: $\$ 15336.33$

Complete the table for the radioactive isotope.Round your answer to two decimal places. \[\begin{array} { | c | c | c | c | } \hline \text { Isotope } & \begin{array} { c } \text { Half-life } \\ \text { (years) } \end{array} & \text { Initial Quantity } & \begin{array} { c } \text { Amount after 1000 } \\ \text { years } \end{array} \\ \hline { } ^ { 226 } \mathrm { Ra } & 1599 & 5 g & --\\ \hline \end{array}\]

A) Amount after 1000 years: $5.24 \mathrm {~g}$ B) Amount after 1000 years: $7.24 \mathrm {~g}$ C) Amount after 1000 years: $3.24 \mathrm {~g}$ D) Amount after 1000 years: $6.24 g$ E) Amount after 1000 years: $4.24 \mathrm {~g}$ A) Amount after 1000 years: $5.24 \mathrm {~g}$ B) Amount after 1000 years: $7.24 \mathrm {~g}$ C) Amount after 1000 years: $3.24 \mathrm {~g}$ D) Amount after 1000 years: $6.24 g$ E) Amount after 1000 years: $4.24 \mathrm {~g}$

Carbon dating presumes that,as long as a plant or animal is alive,the proportion of its carbon that is 14C is constant.The amount of 14C in an object made from harvested plants,like paper,will decline exponentially according to the equation $A = A _ { 0 } e ^ { - 0.0001213 t }$ ,where A represents the amount of 14C in the object,Ao represents the amount of 14C in living organisms,and t is the time in years since the plant was harvested.If an archeological artifact has 30% as much 14C as a living organism,how old would you predict it to be? Round to the nearest year.

A) 28,040 years B) 5715 years C) 9926 years D) 14,758 years E) 100 years A) 28,040 years B) 5715 years C) 9926 years D) 14,758 years E) 100 years

Exam 22: Exponential and Logarithmic Models

Complete the table for a savings account in which interest is compounded continuously. Initial investment Annual rate Time to double Amount after 10 years .... 5.78\% .... \ 10694.82 (Round the answer up to two decimal places. )

(Multiple Choice)

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Question 21

The chemical acidity of a solution is measured in units of pH: $\mathrm { pH } = - \log \left[ \mathrm { H } ^ { + } \right]$ ,where $\left[ \mathrm { H } ^ { + } \right]$ is the hydrogen ion concentration in the solution.If a sample of rain has a pH of 3.4,how many times higher is its $\left[ \mathrm { H } ^ { + } \right]$ than pure water's,which has a pH of 7?

(Multiple Choice)

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Question 22

The chemical acidity of a solution is measured in units of pH: $\mathrm { pH } = - \log \left[ \mathrm { H } ^ { + } \right]$ ,where $\left[ \mathrm { H } ^ { + } \right]$ is the hydrogen ion concentration in the solution.What is $\left[ \mathrm { H } ^ { + } \right]$ if the $\mathrm { pH } = 6.8$ ?

(Multiple Choice)

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Question 23

Find the magnitude R of an earthquake of intensity $\left. I \text { (let } I _ { 0 } = 1 \right)$ . $I = 270300000$

(Multiple Choice)

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Question 24

Сomplete the table for the radioactive isotope. Isotope Half-life (years) Initial Quantity Amount after 1000 years 5715 -- 2

(Multiple Choice)

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Question 25

Complete the table for the radioactive isotope.Round your answer to two decimal places. Isotope Half-life (years) Initial Quantity Amount after 1000 5715 5g --

(Multiple Choice)

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Question 26

A cell site is a site where electronic communications equipment is placed in a cellular network for the use of mobile phones.The numbers of cell sites from 1985 through 2008 can be modeled by $y = \frac { 237,101 } { 1 + 1950 e ^ { - 0.355 t } }$ where t represents the year,with $t = 5$ corresponding to 1985.Use the model to find the numbers of cell sites in the year 2007 .

(Multiple Choice)

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Question 27

Select the correct graph for the given function $y = \frac { 6 } { 1 + e ^ { - 2 x } }$

(Multiple Choice)

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Question 28

Complete the table for a savings account in which interest is compounded continuously. Initial investment Annual rate Time to double Amount after 10 years \7 ,000 \ldots \ldots \ 13143.27 (Round the answer up to two decimal places. )

(Multiple Choice)

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Question 29

Find the exponential model $y = a e ^ { b x }$ that fits the points shown in the table. x 0 3 y 6 1.5

(Multiple Choice)

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Question 30

Complete the table for a savings account in which interest is compounded continuously. Initial investment Annual rate Time to double Amount after 10 years \ 9,000 \ldots 13 \@cdots (Round the answer up to two decimal places. )

(Multiple Choice)

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Question 31

Find the intensity I of an earthquake measuring R on the Richter scale $\left( \text { let } I _ { 0 } = 1 \right)$ . Southern Sumatra,Indonesia in 2007, $R = 8.25$

(Multiple Choice)

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Question 32

Select the correct graph for the given function $y = 7 e ^ { - x / 4 }$

(Multiple Choice)

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Question 33

Complete the table for the radioactive isotope.Round your answer to two decimal places. Isotope Half-life (years) Initial Quantity Amount after 1000 years 1599 5g --

(Multiple Choice)

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Question 34

The population P of a culture of bacteria is described by the equation $P = 1600 e ^ { 0.052 t }$ ,where t is the time,in hours,relative to the time at which the population was 1600. (a)What was the population at $t = 3$ hours? Show your work. (b)After how many hours will the population reach 10000.00? Round to the nearest tenth of an hour.Show your work.

(Essay)

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Question 35

A population growing at an annual rate r will triple in a time t given by the formula $t = \frac { \ln 3 } { r }$ .If the growth rate remains constant and equals 9% per year,how long will it take the population of the town to triple?

(Multiple Choice)

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Question 36

Select a scatter plot of the given data. r 4% 6% 8% 10% 12% 14% T 28)01 18)85 14)27 11)53 9)69 8)38

(Multiple Choice)

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Question 37

Carbon dating presumes that,as long as a plant or animal is alive,the proportion of its carbon that is ¹⁴C is constant.The amount of ¹⁴C in an object made from harvested plants,like paper,will decline exponentially according to the equation $A = A _ { 0 } e ^ { - 0.0001213 t }$ ,where A represents the amount of ¹⁴C in the object,A_o represents the amount of ¹⁴C in living organisms,and t is the time in years since the plant was harvested.If an archeological artifact has 30% as much ¹⁴C as a living organism,how old would you predict it to be? Round to the nearest year.

(Multiple Choice)

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Question 38

An initial investment of $2000 grows at an annual interest rate of 4% compounded continuously.How long will it take to double the investment?

(Multiple Choice)

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Question 39

Select the correct graph for the given function $y = 5 e ^ { - ( x - 2 ) ^ { 2 } / 5 }$

(Multiple Choice)

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Question 40

Exam 22: Exponential and Logarithmic Models

Complete the table for a savings account in which interest is compounded continuously. Initial investment Annual rate Time to double Amount after 10 years .... 5.78\% .... \ 10694.82 (Round the answer up to two decimal places. )

Find the magnitude R of an earthquake of intensity I (let I0=1)\left. I \text { (let } I _ { 0 } = 1 \right)I (let I0​=1) .​ I=270300000I = 270300000I=270300000 ​

Сomplete the table for the radioactive isotope. Isotope Half-life (years) Initial Quantity Amount after 1000 years 5715 -- 2

Complete the table for the radioactive isotope.Round your answer to two decimal places. Isotope Half-life (years) Initial Quantity Amount after 1000 5715 5g --

Select the correct graph for the given function​ y=61+e−2xy = \frac { 6 } { 1 + e ^ { - 2 x } }y=1+e−2x6​ ​

Complete the table for a savings account in which interest is compounded continuously. Initial investment Annual rate Time to double Amount after 10 years \7 ,000 \ldots \ldots \ 13143.27 (Round the answer up to two decimal places. )

Find the exponential model y=aebxy = a e ^ { b x }y=aebx that fits the points shown in the table. x 0 3 y 6 1.5

Complete the table for a savings account in which interest is compounded continuously. Initial investment Annual rate Time to double Amount after 10 years \ 9,000 \ldots 13 \@cdots (Round the answer up to two decimal places. )

Find the intensity I of an earthquake measuring R on the Richter scale ( let I0=1)\left( \text { let } I _ { 0 } = 1 \right)( let I0​=1) . ​ Southern Sumatra,Indonesia in 2007, R=8.25R = 8.25R=8.25 ​

Select the correct graph for the given function​ y=7e−x/4y = 7 e ^ { - x / 4 }y=7e−x/4 ​

Complete the table for the radioactive isotope.Round your answer to two decimal places. Isotope Half-life (years) Initial Quantity Amount after 1000 years 1599 5g --

A population growing at an annual rate r will triple in a time t given by the formula t=ln⁡3rt = \frac { \ln 3 } { r }t=rln3​ .If the growth rate remains constant and equals 9% per year,how long will it take the population of the town to triple? ​

Select a scatter plot of the given data. r 4% 6% 8% 10% 12% 14% T 28)01 18)85 14)27 11)53 9)69 8)38 ​

An initial investment of $2000 grows at an annual interest rate of 4% compounded continuously.How long will it take to double the investment?

Select the correct graph for the given function​ y=5e−(x−2)2/5y = 5 e ^ { - ( x - 2 ) ^ { 2 } / 5 }y=5e−(x−2)2/5 ​

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Hyperbolas

Rotation of Conics

Parametric Equations

Polar Coordinates

Find the magnitude R of an earthquake of intensity $\left. I \text { (let } I _ { 0 } = 1 \right)$ . $I = 270300000$

Select the correct graph for the given function $y = \frac { 6 } { 1 + e ^ { - 2 x } }$

Find the exponential model $y = a e ^ { b x }$ that fits the points shown in the table. x 0 3 y 6 1.5

Find the intensity I of an earthquake measuring R on the Richter scale $\left( \text { let } I _ { 0 } = 1 \right)$ . Southern Sumatra,Indonesia in 2007, $R = 8.25$

Select the correct graph for the given function $y = 7 e ^ { - x / 4 }$

A population growing at an annual rate r will triple in a time t given by the formula $t = \frac { \ln 3 } { r }$ .If the growth rate remains constant and equals 9% per year,how long will it take the population of the town to triple?

Select a scatter plot of the given data. r 4% 6% 8% 10% 12% 14% T 28)01 18)85 14)27 11)53 9)69 8)38

Select the correct graph for the given function $y = 5 e ^ { - ( x - 2 ) ^ { 2 } / 5 }$