To evaluate the function [tex]\( g(x) = 6^x \)[/tex] at [tex]\( x = e \)[/tex], follow these steps:
1. Understand the function: The function [tex]\( g(x) \)[/tex] is an exponential function where the base is [tex]\( 6 \)[/tex]. Therefore, [tex]\( g(x) = 6^x \)[/tex].
2. Identify the value of [tex]\( x \)[/tex]: For this part, we are asked to evaluate the function at [tex]\( x = e \)[/tex]. The constant [tex]\( e \)[/tex] (Euler's number) is approximately [tex]\( 2.71828 \)[/tex].
3. Compute [tex]\( 6^e \)[/tex]:
[tex]\[
g(e) = 6^e \approx 130.3870
\][/tex]
4. Round the result to 4 decimal places: The value of [tex]\( 6^e \)[/tex] rounded to four decimal places is [tex]\( 130.387 \)[/tex].
Therefore,
[tex]\[
g(e) = 130.387
\][/tex]
So, [tex]\( g(e) = 130.387 \)[/tex] when evaluated at [tex]\( x = e \)[/tex].
