The given function is $f(x) = (1.3)^x$.

To calculate $f(-0.5)$, we need to substitute $x = -0.5$ into the function and simplify.

$f(-0.5) = (1.3)^{-0.5}$

Using the property of exponents, $a^{-n} = \frac{1}{a^n}$, we have:

$f(-0.5) = \frac{1}{(1.3)^{0.5}}$

Now, we can compute $(1.3)^{0.5}$ (which is the square root of 1.3) and take the reciprocal.

$f(-0.5) \approx \frac{1}{\sqrt{1.3}} \approx \frac{1}{1.1401754} \approx 0.8760$

So,

$f(-0.5) \approx 0.8760$

Would you like more details or have any questions?

Here are 5 related questions:

1. What is $f(0.5)$ for the function $f(x) = (1.3)^x$?
2. What is the value of $f(0)$ for the same function?
3. How would you compute $f(x)$ for negative values of $x$?
4. What is the inverse of $f(x) = (1.3)^x$?
5. How does changing the base of the exponent affect the shape of the graph of $f(x) = a^x$?

Tip: When dealing with fractional exponents, remember that they represent roots (e.g., $x^{0.5} = \sqrt{x}$).