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Exponential Growth and Decay Word Problems Worksheet with Answers (PDF)

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Exponential Growth and Decay Word Problems Worksheet with Answers (PDF)
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Maria Hernandez

@mariahernandez

·

118 Followers

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This document covers exponential functions, their growth and decay factors, and related problem-solving techniques. It includes formulas, examples, and applications in various real-world scenarios.

• Exponential functions are defined as f(x) = a·bˣ, where b is the base.
• For b > 1, the function exhibits exponential growth; for 0 < b < 1, it shows exponential decay.
• The document covers growth and decay rates, compound interest, and continuous compounding.
• Practical examples include population growth, car depreciation, and radioactive decay.
• Formulas for compound interest and future value calculations are presented.

7/1/2023

347

Section 4.1 Exponential Functions f(x)= a.b* is an exponential function with base b. If bal we have exponential growth. b is the growth fact

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Exponential Functions: Advanced Concepts and Applications

This page continues the discussion on exponential functions, focusing on more advanced concepts and their practical applications. It introduces formulas for compound interest and continuous compounding.

Definition: Compound interest is the addition of interest to the principal sum of a loan or deposit, resulting in interest on interest.

The page presents two key formulas for calculating future value (FV) in compound interest scenarios:

  1. For regular compound interest: FV = P(1 + r/n)^(nt)

    Where:

    • FV = Future Value
    • P = Present Value (initial principal)
    • r = Interest rate (as a decimal)
    • n = Number of times interest is compounded per year
    • t = Number of years

  2. For continuous compounding: FV = Pe^(rt)

    Where:

    • e ≈ 2.71828 (Euler's number)
    • r = Interest rate (as a decimal)
    • t = Time in years

Highlight: The concept of continuous compounding represents the theoretical limit of compound interest, where interest is calculated and added to the principal continuously.

The page includes visual aids and graphs to illustrate the behavior of exponential functions and the differences between various compounding frequencies.

Example: While specific numerical examples are not provided on this page, it's implied that these formulas can be applied to various financial scenarios, such as investment growth or loan repayments.

The document emphasizes the importance of understanding these advanced concepts for more complex financial calculations and modeling of exponential growth in various fields, including economics, biology, and physics.

Section 4.1 Exponential Functions f(x)= a.b* is an exponential function with base b. If bal we have exponential growth. b is the growth fact

View

Exponential Functions: Growth and Decay

This page introduces the concept of exponential functions and their applications in growth and decay scenarios. It provides a comprehensive overview of the fundamental principles and practical examples.

Definition: An exponential function is defined as f(x) = a·bˣ, where 'a' is the initial value and 'b' is the base.

The nature of exponential functions depends on the value of 'b':

  • If b > 1, the function represents exponential growth.
  • If 0 < b < 1, the function represents exponential decay.

Vocabulary:

  • Growth factor: The value of 'b' when b > 1
  • Growth rate: b - 1
  • Decay factor: The value of 'b' when 0 < b < 1
  • Decay rate: 1 - b

Example: In the function f(x) = 5·1.1ˣ, the growth rate is 1.1 - 1 = 0.1 or 10%.

The page includes several practical examples to illustrate the application of exponential functions:

  1. Population Growth: A city with 75,000 people growing at 3% per year.

    Example: P(t) = 75,000 · 1.03ᵗ

  2. Car Depreciation: A car depreciating at 10% per year.

    Example: A(t) = 19,000 · 0.9ᵗ

  3. Radioactive Decay: A substance weighing 250 mg initially, decaying over time.

    Example: y = 250 · 0.933ᵗ

The page also covers methods for finding exponential functions given two points and solving problems involving future values.

Highlight: The document emphasizes the importance of understanding growth and decay factors in real-world applications of exponential functions.

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Compound Interest

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Subjects

/

Pre-Calculus

/

Rational functions

/

Modeling with rational functions

Exponential Growth and Decay Word Problems Worksheet with Answers (PDF)

user profile picture

Maria Hernandez

@mariahernandez

·

118 Followers

Follow

This document covers exponential functions, their growth and decay factors, and related problem-solving techniques. It includes formulas, examples, and applications in various real-world scenarios.

• Exponential functions are defined as f(x) = a·bˣ, where b is the base.
• For b > 1, the function exhibits exponential growth; for 0 < b < 1, it shows exponential decay.
• The document covers growth and decay rates, compound interest, and continuous compounding.
• Practical examples include population growth, car depreciation, and radioactive decay.
• Formulas for compound interest and future value calculations are presented.

7/1/2023

347

 

11th/12th

 

Pre-Calculus

19

Section 4.1 Exponential Functions f(x)= a.b* is an exponential function with base b. If bal we have exponential growth. b is the growth fact

Exponential Functions: Advanced Concepts and Applications

This page continues the discussion on exponential functions, focusing on more advanced concepts and their practical applications. It introduces formulas for compound interest and continuous compounding.

Definition: Compound interest is the addition of interest to the principal sum of a loan or deposit, resulting in interest on interest.

The page presents two key formulas for calculating future value (FV) in compound interest scenarios:

  1. For regular compound interest: FV = P(1 + r/n)^(nt)

    Where:

    • FV = Future Value
    • P = Present Value (initial principal)
    • r = Interest rate (as a decimal)
    • n = Number of times interest is compounded per year
    • t = Number of years

  2. For continuous compounding: FV = Pe^(rt)

    Where:

    • e ≈ 2.71828 (Euler's number)
    • r = Interest rate (as a decimal)
    • t = Time in years

Highlight: The concept of continuous compounding represents the theoretical limit of compound interest, where interest is calculated and added to the principal continuously.

The page includes visual aids and graphs to illustrate the behavior of exponential functions and the differences between various compounding frequencies.

Example: While specific numerical examples are not provided on this page, it's implied that these formulas can be applied to various financial scenarios, such as investment growth or loan repayments.

The document emphasizes the importance of understanding these advanced concepts for more complex financial calculations and modeling of exponential growth in various fields, including economics, biology, and physics.

Section 4.1 Exponential Functions f(x)= a.b* is an exponential function with base b. If bal we have exponential growth. b is the growth fact

Exponential Functions: Growth and Decay

This page introduces the concept of exponential functions and their applications in growth and decay scenarios. It provides a comprehensive overview of the fundamental principles and practical examples.

Definition: An exponential function is defined as f(x) = a·bˣ, where 'a' is the initial value and 'b' is the base.

The nature of exponential functions depends on the value of 'b':

  • If b > 1, the function represents exponential growth.
  • If 0 < b < 1, the function represents exponential decay.

Vocabulary:

  • Growth factor: The value of 'b' when b > 1
  • Growth rate: b - 1
  • Decay factor: The value of 'b' when 0 < b < 1
  • Decay rate: 1 - b

Example: In the function f(x) = 5·1.1ˣ, the growth rate is 1.1 - 1 = 0.1 or 10%.

The page includes several practical examples to illustrate the application of exponential functions:

  1. Population Growth: A city with 75,000 people growing at 3% per year.

    Example: P(t) = 75,000 · 1.03ᵗ

  2. Car Depreciation: A car depreciating at 10% per year.

    Example: A(t) = 19,000 · 0.9ᵗ

  3. Radioactive Decay: A substance weighing 250 mg initially, decaying over time.

    Example: y = 250 · 0.933ᵗ

The page also covers methods for finding exponential functions given two points and solving problems involving future values.

Highlight: The document emphasizes the importance of understanding growth and decay factors in real-world applications of exponential functions.

Similar Content

Pre-Calculus - Compound Interest

Notes about the topic

6

111

0

Know Compound Interest thumbnail

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

13 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying