We are given the function:

\[
g(t) = -3 \cdot 3^{(-t - 2)}
\]

We are tasked with finding \( g(-3) \). To do this, we substitute \( t = -3 \) into the function:

\[
g(-3) = -3 \cdot 3^{(-(-3) - 2)}
\]

First, simplify the exponent:

\[
-(-3) - 2 = 3 - 2 = 1
\]

Now substitute this back into the expression:

\[
g(-3) = -3 \cdot 3^1 = -3 \cdot 3 = -9
\]

Thus, the value of \( g(-3) \) is:

\[
g(-3) = -9
\]

Would you like further details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How would the function change if we modified the base of the exponent from 3 to another number?
2. Can you find \( g(2) \) using the same function?
3. What happens to the function as \( t \to \infty \)?
4. How does the negative sign outside the function affect the graph of \( g(t) \)?
5. Can you rewrite the function in a logarithmic form?

**Tip:** Always simplify the exponent before applying powers to avoid mistakes in calculations.

Learn how to evaluate the exponential function g(t) = -3 * 3^(-t - 2) by substituting t = -3. This problem demonstrates key mathematical concepts such as exponent simplification and substitution, suitable for students in Grades 9-10.

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