Answered

Expand your knowledge base with the help of IDNLearn.com's extensive answer archive. Discover in-depth answers to your questions from our community of experienced professionals.

Evaluate [tex]\( f(x) = e^x \)[/tex] when [tex]\( x = -3 \)[/tex]. Round your answer to the nearest hundredth.

Sagot :

GinnyAnsweridn
To evaluate the function [tex]\( f(x) = e^x \)[/tex] at [tex]\( x = -3 \)[/tex], we need to follow these steps:

1. Substitute [tex]\(-3\)[/tex] into the function: We have [tex]\( f(-3) = e^{-3} \)[/tex].

2. Compute [tex]\( e^{-3} \)[/tex]: The value of [tex]\( e^{-3} \)[/tex], which means raising the mathematical constant [tex]\( e \)[/tex] (approximately equal to 2.71828) to the power of [tex]\(-3\)[/tex], is approximately [tex]\( 0.049787068367863944 \)[/tex].

3. Round the result: To round this result to the nearest hundredth, we look at the thousandths place (which is the third decimal place). If it is 5 or greater, we round the second decimal place up. In this case, the third decimal place is 9, so we round up.

4. Final rounded result: [tex]\( 0.049787068367863944 \)[/tex] rounded to the nearest hundredth is [tex]\( 0.05 \)[/tex].

Thus, the value of [tex]\( f(-3) = e^{-3} \)[/tex] rounded to the nearest hundredth is [tex]\( 0.05 \)[/tex].
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Your search for answers ends at IDNLearn.com. Thank you for visiting, and we hope to assist you again soon.