To solve this problem, we need to evaluate the function $q(x) = 15 \times 3^x$ for the values $x = -1$, $x = 0$, and $x = 1$ to see which table matches the results.

Step-by-Step Calculation:

1. For $x = -1$: $q(-1) = 15 \times 3^{-1} = 15 \times \frac{1}{3} = 5$

2. For $x = 0$: $q(0) = 15 \times 3^0 = 15 \times 1 = 15$

3. For $x = 1$: $q(1) = 15 \times 3^1 = 15 \times 3 = 45$

Summary of Results:

• $q(-1) = 5$
• $q(0) = 15$
• $q(1) = 45$

Matching with the Options:

Now, let's compare these values to the tables provided in the image.

• Option A: Does not match, as it lists $q(-1) = -45$, $q(0) = 0$, and $q(1) = 45$.
• Option B: Does not match, as it lists $q(-1) = \frac{1}{5}$, $q(0) = 3$, and $q(1) = 45$.
• Option C: Does not match, as it lists $q(-1) = \frac{1}{5}$, $q(0) = 15$, and $q(1) = 45$.
• Option D: Matches, as it lists $q(-1) = 5$, $q(0) = 15$, and $q(1) = 45$.

Conclusion:

The correct answer is Option D.

Would you like further clarification on any step? Here are some additional questions you might consider:

1. How is exponential growth reflected in the function $q(x) = 15 \times 3^x$?
2. What would happen to the function if the base changed from 3 to another number?
3. Why does $q(0)$ equal the initial multiplier, 15, in this function?
4. How does changing the exponent value (e.g., from $x$ to $2x$) affect the output values?
5. What is the impact of a negative exponent on the value of the function?

Tip: When working with exponential functions, remember that negative exponents create fractional values (as seen with $3^{-1} = \frac{1}{3}$).