To evaluate the expression $e^{-\frac{1}{900} \times 6}$, we first simplify the exponent:

$-\frac{1}{900} \times 6 = -\frac{6}{900} = -\frac{1}{150}$

Thus, the expression becomes:

$e^{-\frac{1}{150}}$

Now, using an approximation for $e^{-\frac{1}{150}}$:

$e^{-\frac{1}{150}} \approx 0.99335$

So, the value of $e^{-\frac{1}{150}}$ is approximately 0.99335.

Would you like more details or have any other questions?

Here are 5 related questions:

1. What is the general formula for the exponential function $e^x$?
2. How does the value of $e^{-x}$ change as $x$ increases?
3. Can you approximate $e^{-1/150}$ using a series expansion of $e^x$?
4. What is the importance of the base $e$ in calculus?
5. How do exponential functions behave in real-world applications like population growth or decay?

Tip: In calculus, exponential decay functions like $e^{-x}$ are frequently used to model things that decrease over time, such as radioactive decay.