It looks like you're trying to differentiate between exponential growth and exponential decay. Here's a structured breakdown for each:
Exponential Growth
- Description: An amount increases exponentially at a constant rate over time.
- Example: Populations of organisms, such as bacteria or animals, can grow exponentially when resources are abundant.
- Constant Rate: The growth rate remains constant over each time interval, leading to faster increases as time progresses.
Exponential Decay
- Description: An amount decreases exponentially at a constant rate over time.
- Example: The decay of radioactive substances, where the quantity reduces by a consistent percentage over each time interval.
- Constant Rate: The decay rate remains constant, which means that the quantity decreases more significantly in the beginning and slows down as the amount remaining becomes smaller.
If you need help with more specific examples or concepts related to these functions, feel free to ask!