To solve this problem, we need to analyze the function $q(x) = 15 \cdot 3^x$ and calculate the values of $q(x)$ for the given values of $x$ in each table option.

Step-by-Step Solution

1. Given Function: $q(x) = 15 \cdot 3^x$.

2. Calculate $q(x)$ for Different Values of $x$:

   • When $x = -1$: $q(-1) = 15 \cdot 3^{-1} = 15 \cdot \frac{1}{3} = 5$

   • When $x = 0$: $q(0) = 15 \cdot 3^0 = 15 \cdot 1 = 15$

   • When $x = 1$: $q(1) = 15 \cdot 3^1 = 15 \cdot 3 = 45$

3. Matching Calculated Values to Options:

   Using our calculated values:

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

   Let's examine each option to see which one matches these values:

   • Option A: $q(-1) = -45$, $q(0) = 0$, $q(1) = 45$ — does not match.
   • Option B: $q(-1) = \frac{1}{5}$, $q(0) = 3$, $q(1) = 45$ — does not match.
   • Option C: $q(-1) = 5$, $q(0) = 15$, $q(1) = 45$ — matches our calculations.
   • Option D: $q(-1) = 5$, $q(0) = 15$, $q(1) = 45$ — matches as well.

4. Conclusion: Options C and D both contain the correct values for $q(x)$. Thus, both C and D are correct choices.

Would you like further explanation or have any questions?

Additional Questions

1. How would the values change if the base of the exponent was different, for example, $q(x) = 15 \cdot 2^x$?
2. What happens to the function $q(x)$ as $x$ becomes increasingly negative?
3. Can we determine the nature of this function (increasing or decreasing) just from the formula $q(x) = 15 \cdot 3^x$?
4. How would this function look graphically for $x$ in the range $[-2, 2]$?
5. How would the answers change if the multiplier was different, for instance, $q(x) = 10 \cdot 3^x$?

Tip

In exponential functions of the form $f(x) = a \cdot b^x$, $a$ is the initial value when $x = 0$, and $b$ determines the growth rate if $b > 1$ or decay if $0 < b < 1$.