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The image you have provided shows a series of exponential functions. Let's break them down and solve or analyze them individually:

### Problem 11:
\[
f(x) = 5^{-x}
\]
This is an exponential function where the base is 5, and the exponent is \(-x\). 

### Problem 12:
\[
h(x) = 10^{-x}
\]
This is an exponential function with base 10 and exponent \(-x\).

### Problem 13:
\[
h(x) = \left(\frac{5}{4}\right)^x
\]
Here, we have an exponential function with base \(\frac{5}{4}\) and exponent \(x\).

### Problem 14:
\[
g(x) = \left(\frac{3}{2}\right)^x
\]
This is an exponential function with base \(\frac{3}{2}\) and exponent \(x\).

### Problem 15:
\[
g(x) = \left(\frac{5}{4}\right)^{-x}
\]
This exponential function has base \(\frac{5}{4}\), but the exponent is negative, making it equivalent to:
\[
g(x) = \frac{1}{\left(\frac{5}{4}\right)^x} = \left(\frac{4}{5}\right)^x
\]

### Problem 16:
\[
f(x) = \left(\frac{3}{2}\right)^{-x}
\]
This function is similar to problem 14, except the exponent is negative. This can be rewritten as:
\[
f(x) = \left(\frac{2}{3}\right)^x
\]

---

Do you need detailed steps for solving these problems? Feel free to ask for more clarification on any specific function.

Here are 5 questions based on the problems:
1. How do exponential functions behave as \(x\) increases or decreases?
2. What happens when the base of an exponential function is a fraction less than 1?
3. How do negative exponents affect the graph of an exponential function?
4. What are the key differences between exponential growth and decay?
5. How would you solve for \(x\) when \(f(x)\) equals a particular value?

**Tip:** Exponential functions with positive exponents grow rapidly, while those with negative exponents decay quickly, especially if the base is greater than 1.

Solve the following exponential functions: f(x) = 5^(-x), h(x) = 10^(-x), h(x) = (5/4)^x, g(x) = (3/2)^x, g(x) = (5/4)^(-x), f(x) = (3/2)^(-x)

Learn how to solve exponential functions involving negative exponents and fractional bases such as f(x) = (5/4)^(-x) and g(x) = (3/2)^x. This guide covers the properties of exponents and provides step-by-step solutions for exponential growth and decay problems, ideal for students in Grades 9-11.

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