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.