https://file.aiquickdraw.com/mathbot/file/1726509803732t99h9bo8.jpg

The question asks for situations that model **exponential decay**, which refers to a process where a quantity decreases at a rate proportional to its current value. 

In the provided choices:

1. **An investment that earns 5.99% annually compounded monthly** - This represents **exponential growth**, not decay, since the investment is increasing in value.
2. **The value of an automobile, which depreciates 15% each year** - This is a case of **exponential decay**, as the value is decreasing by a fixed percentage annually.
3. **A fish population that doubles every three months** - This describes **exponential growth**, not decay, since the population is increasing.
4. **The half-life of an element** - This is a classic example of **exponential decay**, where the quantity of the element decreases by half over a consistent time interval.
5. **The outbreak of an illness, which increases every two weeks** - This describes **exponential growth**, as the number of infected individuals is increasing.
6. **Algae in a pond, which increases over a month** - This also describes **exponential growth**, as the algae population is increasing.

Thus, the correct choices that model **exponential decay** are:
- **The value of an automobile, which depreciates 15% each year**
- **The half-life of an element**

Would you like further explanation on any part of this? Here are 5 related questions to expand on this topic:

1. What is the formula for exponential decay and how is it applied?
2. How does exponential decay differ from linear decay?
3. Can you provide more real-world examples of exponential decay?
4. How does the rate of decay affect the time it takes for a substance to reach half its initial value?
5. How is exponential growth different from exponential decay in terms of mathematical modeling?

**Tip:** Exponential decay can be modeled by the equation \( N(t) = N_0 e^{-kt} \), where \( N_0 \) is the initial amount, \( k \) is the decay constant, and \( t \) is time.

Which of the following situations model exponential decay? Select 2 choice(s)

Learn how to identify situations that model exponential decay, such as the value depreciation of an automobile and the half-life of an element. This problem is suitable for students in Grades 9-12 and covers key concepts in exponential decay and related formulas.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation