The problem asks you to evaluate the function $f(x) = 10^{-x}$ at $x = 3$ and identify whether it represents a growth or decay function.

1. Substitute $x = 3$ into the function: $f(3) = 10^{-3}$

2. Calculate $10^{-3}$: $10^{-3} = \frac{1}{10^3} = \frac{1}{1000} = 0.001$

Thus, $f(3) = 0.001$.

Growth or Decay:

Since the exponent on 10 is negative, the function $f(x) = 10^{-x}$ decreases as $x$ increases, meaning it represents an exponential decay function.

The answer is: $f(3) = 0.001$

Would you like further clarification on exponential growth and decay?

Here are some related questions:

1. What is the general form of an exponential decay function?
2. How does the base of the exponential function affect the rate of growth or decay?
3. How would you graph the function $f(x) = 10^{-x}$?
4. What is the difference between $f(x) = 10^x$ and $f(x) = 10^{-x}$ in terms of their behavior?
5. Can the function $f(x) = 10^{-x}$ ever reach zero?

Tip: In exponential decay, as the exponent becomes larger, the function approaches zero but never quite reaches it!