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

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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].
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