To determine which of the given options represents [tex]\( e^{-4} \)[/tex] rounded to the nearest thousandth, let's proceed through the following steps:
1. Understand what [tex]\( e^{-4} \)[/tex] means:
- [tex]\( e \)[/tex] is the base of the natural logarithm, approximately equal to 2.71828.
- [tex]\( e^{-4} \)[/tex] means we are raising [tex]\( e \)[/tex] to the power of -4.
2. Calculate [tex]\( e^{-4} \)[/tex]:
- The value of [tex]\( e^{-4} \)[/tex] is approximately 0.0183156.
3. Round the result to the nearest thousandth:
- To round to the nearest thousandth, we look at the fourth decimal place.
- In this case, 0.0183156 rounds to 0.018 when rounded to the nearest thousandth.
4. Compare with the given options:
- A. 54.598
- B. 10.873
- C. 0.018
- D. 1.645
The correct option is the one that matches our rounded value:
Thus, C. 0.018 represents [tex]\( e^{-4} \)[/tex] rounded to the nearest thousandth.
The answer is option 3.
