## Exponential Decay

#### Aligned To Common Core Standard:

**Building Functions** - HSF-BF.A.1b

**What is Exponential Decay?** - Exponential decay is defined as the process of decline in an amount by a constant percentage over some time. Mathematically, it is expressed as,
y = a(1 -b)^{x}
Where, **y** is defined as the final amount, **a** represents the original amount, **b** is the decay factor and, **x** represents the amount of passed time.
Exponential decay differs from linear decay in terms of decay factor. In the linear function, the original number is decreased by the same amount every time. However, in exponential decay, the decrease in the original amount changes over time. That means the decay factor depends on a certain percentage of the original amount.
**The Exponential Decay Formula** - To fully understand the exponential decay formula, it is important to understand and identify each of its components
y = a(1 -b)^{x}
Let's properly define and understand each of its elements:
**Decay factor (b)** - Decay factor is defined as the percentage decrease of the original amount
**Original Amount (a)** - The original amount is the amount before the occurrence of decay. For example, the original amount is the number of cherries a bakery buys, and the exponential factor is the percentage of used apples every hour to bake cherry pies.
**The exponential decay (x)** - The 'x' written as the exponent represents the exponential decay. Exponential decay is always expressed in time. It shows the frequency of the decay and is usually stated in seconds, minutes, hours, days, or years.
These worksheets and lessons will help students learn how to calculate and use the concept of exponential decay in many different practical applications.

### Printable Worksheets And Lessons

- Sam's Car Value Step-by-step
Lesson- I'm pretty sure that most cars depreciate at 25% or
greater per year. Sam's car must be great!

- Guided Lesson
- Let's investigate Zoe's cell phone dilemma, determine an exponential
decay model, and Jacob buys a wallet.

- Guided Lesson Explanation
- You might see me use the word "hub" in word problems
at time. It comes from my days that I moonlighted in insurance sales.

- Practice Worksheet
- A really nice mix of problems to put your mind to.

- Matching Worksheet
- That is one expensive hand blender and pan drive!

#### Homework Sheets

Man! After 3 years laptops are worth less than expensive cups of coffee.

- Homework 1 - Kelly purchased a laptop worth $5,000 in the year 2003. It loses its value by 10% per year. What is the value of the laptop in 2007?
- Homework 2 - Mathew bought an aquarium worth $400 in the first week of the year. Its value depreciates by 3% per week. What will the value of fish aquarium after 8 weeks?
- Homework 3 - Which of the following model is an exponential decay model?

#### Practice Worksheets

Doing lots of depreciation problems is pretty depressing. Mix in a few exponential growth problems, when you get the chance.

- Practice 1 - Kylee purchased a mobile phone amplifier worth $3,000 in the year 2001. It loses its value by 10% per year. What is the value of the amplifier in 2006?
- Practice 2 - Allison bought a refrigerator for $3,500 in the year 2007. It loses its value by 10% per year. What is the value of the Refrigerator in 2013?
- Practice 3 - Allie purchased a microwave worth $200 in the year 2007. It loses its value by 7% per year. What is the value of the television in 2010?

#### Math Skill Quizzes

Half of the problems ask you to identify the exponential decay model.

- Quiz 1 - Allen purchased an Iphone worth $700 in the year 2005. It loses its value by 11% per year. What is the value of the iphone in 2008?
- Quiz 2 - Audrey bought a BMW for $7,500 in the year 2007. It loses its value by 10% per year. What is the value of the BMW in 2012?
- Quiz 3 - Audrey bought a sofa for $259 in the year 2009. It loses its value by 10% per year. What is the value of the sofa in 2012?