https://file.aiquickdraw.com/mathbot/file/1725553875870kczr92b0.jpg

answer the question in the pic with graph

Here are the graphs of the functions:

1. \( f(x) = 6^x \) (blue) – an exponential growth function, rapidly increasing as \( x \) becomes positive.
2. \( f(x) = 5^{-x} \) (red) – an exponential decay function, decreasing quickly as \( x \) increases.
3. \( f(x) = e^{-x} \) (green) – another exponential decay function, but less steep than the red curve due to the base \( e \).

Each graph reflects either growth (for positive exponents) or decay (for negative exponents), depending on the function.

Would you like further details or have any questions?

Here are 5 related questions for deeper understanding:
1. How do exponential growth and decay functions behave as \( x \to -\infty \)?
2. What is the effect of changing the base of the exponent on the graph?
3. How do the graphs of \( e^x \) and \( e^{-x} \) compare?
4. What applications do exponential functions have in real-world scenarios?
5. How do exponential functions relate to logarithmic functions?

**Tip:** Exponential functions with negative exponents are always decreasing functions for \( x > 0 \).

Answer the question in the pic with graph

Explore the behavior of exponential growth and decay by graphing the functions 6^x, 5^-x, and e^-x. Understand how different bases affect the steepness and direction of exponential functions, suitable for students in Grades 9-12.

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