Here's how to understand the problem and the solution:
* Understanding e^(-x)
* e is Euler's number, approximately equal to 2.71828.
* e^(-x) is the exponential function with a negative exponent. This means the value will be less than 1 and will decrease as x increases.
* Finding the Range
* Since x is between 2 and 3, we need to find the values of e^(-2) and e^(-3).
* Using a calculator:
* e^(-2) ≈ 0.1353
* e^(-3) ≈ 0.0498
* Conclusion
* The real value of e^(-x) between 2 and 3 is between approximately 0.0498 and 0.1353.
In other words, as x goes from 2 to 3, e^(-x) decreases from about 0.1353 to about 0.0498.
