https://file.aiquickdraw.com/mathbot/file/1722523801588ooky15ch.jpg

To solve the problem, let's start by understanding the information given:

1. The value of \( q(x) \) decreases by 45% for every increase in \( x \) by 1.
2. \( q(0) = 14 \).

When a value decreases by 45%, it retains 55% of its original value. Mathematically, this can be written as:

\[ q(x) = q(0) \cdot (0.55)^x \]

Since \( q(0) = 14 \):

\[ q(x) = 14 \cdot (0.55)^x \]

Thus, the equation that defines \( q \) is:

\[ q(x) = 14 \cdot (0.55)^x \]

Comparing this with the provided options, we see that the correct answer is:

\[ \boxed{\text{C) } q(x) = 14(0.55)^x} \]

Would you like a detailed explanation or have any questions about this solution? Here are some related questions you might find interesting:

1. How do you derive the formula for exponential decay?
2. What are some real-life applications of exponential decay?
3. How do you solve exponential equations with different bases?
4. How does exponential decay differ from exponential growth?
5. What is the general form of an exponential function?
6. How can you determine the half-life of a substance using exponential decay?
7. How do you graph an exponential decay function?
8. What are some common mistakes when solving exponential decay problems?

**Tip:** When dealing with exponential functions, always pay attention to the base. A base less than 1 indicates decay, while a base greater than 1 indicates growth.

Learn how to solve an exponential decay problem involving the function q(x) = 14 * (0.55)^x. Understand the concept of exponential decay and how to apply it in mathematical problems. Suitable for high school students and those interested in exponential functions.

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