5. Exponential and Logarithmic Functions

Evaluate Functions with Base e

Exponential Functions

Evaluate Exponential Functions: Base e

Graph f(x) = 2^x and its inverse function in the same rectangular coordinate system.

In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. 3^√5

Using a calculator to evaluate exponential expressions involving base e

Graph exponential growth functions

In Exercises 47–52, graph functions f and g in the same rectangular coordinate system. Graph and give equations of all asymptotes. If applicable, use a graphing utility to confirm your hand-drawn graphs. f(x) = 3^x and g(x) = 3^-x

In Exercises 19–24, the graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 3^x, g(x) = 3^(x-1), h(x) = 3^x - 1 ; f(x) = -3^x, G(x) = 3^(-x), H(x) = -3^(-x) <img src="https://lightcat-files.s3.amazonaws.com/problem_images/310da44985300604-1675890982364.jpg" alt="" />

Finding an Interest Rate to Match Certain Financial Goals, Ex 3

In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. e^2.3

In Exercises 25-34, begin by graphing f(x) = 2^x. Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. g(x) = 2.2^x

In Exercises 25-34, begin by graphing f(x) = 2^x. Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. h(x) = 2^(x+1) – 1

Deriving the Compound Interest Formula

In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. f(x) = (0.6)^x

Compound Interest Example - Find Starting Principal

Transformation of an Exponential Function / Example 14.5

In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. 4^-1.5

Use the compound interest formulas A = P (1+ r/n)^nt and A =Pe^rt to solve exercises 53-56. Round answers to the nearest cent. 
Find the accumulated value of an investment of $10,000 for 5 years at an interest rate
of 1.32% if the money is
a. compounded semiannually;
b. compounded quarterly;
c. compounded monthly;
d. compounded continuously.

Evaluating an exponential function with base e that models a real world situation

In Exercises 47–52, graph functions f and g in the same rectangular coordinate system. Graph and give equations of all asymptotes. If applicable, use a graphing utility to confirm your hand-drawn graphs. f(x) = 3^x and g(x) = (1/3). 3^x

In Exercises 61–64, give the equation of each exponential function whose graph is shown. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/35852ad21589f816-1675892065917.jpg" alt="" /><img class="fr-dib" src="https://lightcat-files.s3.amazonaws.com/problem_images/0ef937c3aa7ad804-1678176795060.jpg" style="width: 300px;">

The figure shows the graph of f(x) = e^x. In Exercises 35-46, use transformations of this graph to graph each function. Be sure to give equations of the asymptotes. Use the graphs to determine graphs. each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn  h(x) = e^(x-1)+2

Graph of an Exponential Function

In Exercises 19–24, the graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 3^x, g(x) = 3^(x-1), h(x) = 3^x - 1 ; f(x) = -3^x, G(x) = 3^(-x), H(x) = -3^(-x) <img src="https://lightcat-files.s3.amazonaws.com/problem_images/e94785f40a19ab58-1675888511854.jpg" alt="" />

Understanding Simple Interest and Compound Interest

Finding an Interest Rate to Match Certain Financial Goals, Ex 1

Evaluate Exponential Functions with Base e

Transformation of an Exponential Function / Example 14.3

Find compound interest using an investment model

Finding the Equation of an Exponential Function

Graphing Exponential Functions

Deriving the Annual Compound Interest Formula

Radioactive Decay and Exponential Growth

In Exercises 19–24, the graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 3^x, g(x) = 3^(x-1), h(x) = 3^x - 1 ; f(x) = -3^x, G(x) = 3^(-x), H(x) = -3^(-x) <img src="https://lightcat-files.s3.amazonaws.com/problem_images/fd087fe7aee9be99-1676959990708.jpg" alt="" />

Exponential Growth / Population Growth Problem.

In Exercises 1–4, the graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 4^x, g(x) = 4^-x, h(x) = -4^(-x), r(x) = -4^(-x)+3 3. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/5f10c558bc362f89-1671819593011.jpg" alt="" />

In Exercises 5–9, graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function’s domain and range. f(x) = e^x and g(x) = 2e^(x/2)

In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. f(x) = 4^x

In Exercises 25-34, begin by graphing f(x) = 2^x. Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. g(x) = 2^x – 1

Deriving the Continuous Compounding Formula

Evaluate Exponential Functions at Given Values

In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. 2^3.4

Identify the Exponential Function

The figure shows the graph of f(x) = e^x. In Exercises 35-46, use transformations of this graph to graph each function. Be sure to give equations of the asymptotes. Use the graphs to determine graphs. each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn  g(x) = e^x+2

In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. g(x) = (3/2)^x

In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. h(x) = (1/2)^x

The figure shows the graph of f(x) = e^x. In Exercises 35-46, use transformations of this graph to graph each function. Be sure to give equations of the asymptotes. Use the graphs to determine graphs. each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn  h(x) = e^2x + 1

Solving a Continuous Compounding Problem

Transformation of an Exponential Function / Example 14.4

Compound Interest - More than Once Per Year

Graph of y = e ^ (x + 3) using Graph Transformations

Use the compound interest formulas to solve Exercises 10–11. Suppose that you have $5000 to invest. Which investment yields the greater return over 5 years: 1.5% compounded semiannually or 1.45% compounded monthly?

In Exercises 25-34, begin by graphing f(x) = 2^x. Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. g(x) = −2^x

The figure shows the graph of f(x) = e^x. In Exercises 35-46, use transformations of this graph to graph each function. Be sure to give equations of the asymptotes. Use the graphs to determine graphs. each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn  g(x) = 2e^x

Graph exponential decay functions

The figure shows the graph of f(x) = e^x. In Exercises 35-46, use transformations of this graph to graph each function. Be sure to give equations of the asymptotes. Use the graphs to determine graphs. each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn  h(x) = e^-x

In Exercises 1–4, the graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 4^x, g(x) = 4^-x, h(x) = -4^(-x), r(x) = -4^(-x)+3 1. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/ed6ab88e198af581-1671818346246.jpg" alt="" />

In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. e^-0.95

In Exercises 5–9, graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function’s domain and range. f(x) = 3^x and g(x) = -3^x

Compare exponential models using properties of exponents

Evaluating and Graphing Exponential Functions

Graphing Exponential Functions w/ Graph Transformations

In Exercises 25-34, begin by graphing f(x) = 2^x. Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. g(x) = 2^(x+1)

Use the compound interest formulas A = P (1+ r/n)^nt and A =Pe^rt to solve exercises 53-56. Round answers to the nearest cent. Suppose that you have $12,000 to invest. Which investment yields the greater return over 3 years: 0.96% compounded monthly or 0.95% compounded continuously?

Finding an Interest Rate to Match Certain Financial Goals, Ex 2

Learn the toughest concepts covered in Algebra with step-by-step video tutorials and practice problems by world-class tutors

College Algebra

https://static.studychannel.pearsonprd.tech/courses/college-algebra/thumbnails/college-algebra

#FFFFFF

patrickJMT

Professor Dave Explains

larryschmidt

KSpinMATH

LearnZillion

Mr. G

Mathispower4u

1. Fundamental Concepts of Algebra

2. Equations and Inequalities

3. Functions and Graphs

4. Polynomial and Rational Functions

6. Systems of Equations and Inequalities

7. Matrices and Determinants

8. Conic Sections

9. Sequences, Induction, and Probability

undefined - Channels

Expand Logarithmic Expressions

Condense Logarithmic Expressions

The Change-of-Base Property

Properties of Logarithms

Use Like Bases to Solve Exponential Equations

Use Logarithms to Solve Exponential Equations

Use the Definition of a Logarithm to Solve Logarithmic Equations

Use the One-to-One Property of Logarithms to Solve Equations

Solve Problems Using Exponential and Logarithmic Equations

Exponential and Logarithmic Equations

Evaluate & Graph Exponential Functions

Use Compound Interest Formulas

Model Exponential Growth and Decay

Use Logistic Growth Models

Choose an Appropriate Model for Data

Express an Exponential Model in Base e

Exponential Growth and Decay

Change From Logarithmic to Exponential Form

Change From Exponential to Logarithmic Form

Evaluate Logarithms

Use Basic Logarithmic Properties

Graph Logarithmic Functions

Use Common Logarithms

Logarithmic Functions

General Chemistry

Jules

Study the key concepts of Physics with descriptive videos, questions, and more

Physics

Patrick

General Biology

Jason

Financial Accounting

Brian

Dive deep into Psychology with videos, practice problems, and more.

Psychology

Microeconomics

The first in a two-course sequence introduces the basic structure and functions of the human body

Anatomy & Physiology

College Algebra covers algebraic topics and skills necessary to succeed in college-level math

Organic Chemistry

Johnny

Genetics

Kylia

GOB Chemistry

Microbiology

Cell Biology

Analytical Chemistry

Study topics incliding trogonometric functions, identities and equations, solutions of triangles, complex numbers, and other topics as time permits

Trigonometry

Learn the toughest concepts covered in Precalculus with step-by-step video tutorials and practice problems by world-class tutors

Precalculus

Biochemistry

Macroeconomics

Chemistry

Biology

Math

Business

Social Sciences

Michelle Barry Franco

Building Great Presentations

Eric Zackrison, PhD

Critical Thinking And Problem Solving

Sam Bennett

Embracing Times Of Uncertainty

Nicole Tetreault, PhD

Emotional Intelligence Basics

Eugene Choi, PharmD

Enhancing Your Critical Thinking Skills

Jason Richardson, PsyD

Habits To Win Every Day

Alyssa Lowery, PhD

Having Powerful Advanced Conversations

Don Gilman, EdD

How To Influence & Persuade

Amy Matthews

Leadership Skills For Rising Stars

Listening To Lead

Michael Shermer, PhD

Making Decisions Under Uncertainty

Lynne Hurdle

Mistakes To Avoid When Resolving Conflict

Michael Veltri

Overcoming Decision Making Traps

Mike Vardy

Prioritizing Effectively

Secrets Of Effective Prioritization

Strategies To Build Up Your Creativity

Tools For Decision Making

Tutti Taygerly

Unleash And Advance Your Creativity

Winning Collaboration: How To Work More Effectively With Different Personalities