https://file.aiquickdraw.com/mathbot/file/1726582166659c4d69wx7.jpg

The problem on your screen involves finding the correct equation to represent the decay of an ant population over time, where the population decreases by 8% per hour.

Let's break it down:

1. The initial population is **64,000 ants**.
2. The population decreases by **8% per hour**, meaning 92% (or 0.92) of the population remains after each hour.

This represents exponential decay, which can be modeled by the equation:

\[
y = P(1 - r)^t
\]

Where:
- \(P\) is the initial population (64,000 ants),
- \(r\) is the rate of decay (0.08),
- \(t\) is the time in hours.

Therefore, the equation becomes:

\[
y = 64000(0.92)^x
\]

This matches option **C**.

Would you like further details or have any questions?

Here are 5 related questions you can explore:

1. What happens if the decay rate changes to 10%?
2. How would the equation change if the initial population were different?
3. What does the base of the exponential function represent in this context?
4. How can you calculate the number of ants after 5 hours?
5. How does exponential decay differ from linear decay?

**Tip:** In exponential decay problems, always check the percentage of the remaining population and ensure it correctly matches the base of the exponential function.

An exterminator estimates that a house has approximately 64,000 ants. After treating the house with a repellent, the ant population decreases at a rate of 8% per hour. Which equation represents this situation where y is the number of ants remaining after x hours?

Solve an exponential decay problem where an exterminator treats a house, and the ant population decreases by 8% per hour. Learn how to represent the remaining ants with the equation y = 64000(0.92)^x. Suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation